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Deck 4: Polynomial Functions
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Question
Determine the vertex of the graph of the quadratic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
From the graph of the quadratic function 
, determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
Question
Write the quadratic function 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
Question
Write the standard form of the equation of the parabola that has a vertex at 
and passes through the point 
.
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
Question
Write the standard form of the equation of the parabola that has a vertex at 
and passes through the point 
.
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
Question
Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 280.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Compare the graph of 
with 
.
A)
shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9.
B)
shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9.
C)
shifts right 7 units, shifts downward 5 units, and shrinks by a factor of 
)
D)
shifts right 7 units, shifts upward 5 units, and shrinks by a factor of 
)
E)
shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9.
with .A)
shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9.B)
shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9.C)
shifts right 7 units, shifts downward 5 units, and shrinks by a factor of )
D)
shifts right 7 units, shifts upward 5 units, and shrinks by a factor of )
E)
shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9. Question
Describe the right-hand and the left-hand behavior of the graph of 
.
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
.A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
Question
Find two positive real numbers whose product is a maximum and whose sum is 156.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The height, 
, of a punted rugby ball is given by 
where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?
A)
B)
C)
D)
E)
, of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?A)
B)
C)
D)
E)
Question
From the graph of the quadratic function 
, determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
Question
A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the quadratic function 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Compare the graph of 
with 
.
A)
- 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of 
)
B)
- 8 shifts right 4 units, shifts upward 8 units, and shrinks by a factor of 
)
C)
- 8 shifts left 16 units, shifts upward 8 units, and shrinks by a factor of 
)
D)
- 8 shifts right 16 units, shifts upward 8 units, and shrinks by a factor of 
)
E)
- 8 shifts right 4 units, shifts downward 8 units, and shrinks by a factor of 
)
with .A)
- 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of )
B)
- 8 shifts right 4 units, shifts upward 8 units, and shrinks by a factor of )
C)
- 8 shifts left 16 units, shifts upward 8 units, and shrinks by a factor of )
D)
- 8 shifts right 16 units, shifts upward 8 units, and shrinks by a factor of )
E)
- 8 shifts right 4 units, shifts downward 8 units, and shrinks by a factor of )
Question
Determine the x-intercept(s) of the quadratic function 
.
A)
B)
C)
D)
E) no x-intercept(s)
.A)
B)
C)
D)
E) no x-intercept(s)
Question
Determine the x-intercept(s) of the quadratic function 
.
A)
B)
C) no x-intercept(s)
D)
E)
.A)
B)
C) no x-intercept(s)
D)
E)
Question
Write the quadratic function 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
Question
A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is 
, express the area, A, as a function of the width, x, of the window. 
A)
B)
C)
D)
E)
, express the area, A, as a function of the width, x, of the window. A)
B)
C)
D)
E)
Question
Find the standard form of the quadratic function shown below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Using a graphing utility, graph 
and approximate the zeros and their multiplicity.
A)
B)
C)
D)
E)
and approximate the zeros and their multiplicity.A)
B)
C)
D)
E)
Question
Write 
in the form 
when 
.
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
Question
Find all real zeros of the polynomial 
and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
Question
If 
, use synthetic division to evaluate 
.
A)
B)
C)
D)
E)
, use synthetic division to evaluate .A)
B)
C)
D)
E)
Question
An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by 
, determine the domain of 
. 
A)
B)
C)
D)
E)
, determine the domain of . A)
B)
C)
D)
E)
Question
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Question
Find all real zeros of the polynomial 
and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
Question
Describe the right-hand and the left-hand behavior of the graph of 
.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
.A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
Question
Find all real zeros of the polynomial 
and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
Question
Describe the right-hand and the left-hand behavior of the graph of 
.
A) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
.A) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
Question
An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
in the form 
when 
, and demonstrate that 
.
in the form when , and demonstrate that . Question
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Question
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Question
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Use the zero or root feature of a graphing utility to approximate the zeros of 
accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Question
Given 
is a root, determine all other roots of 
.
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
Question
Use the zero or root feature of a graphing utility to approximate the zeros of the function 
accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
Question
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Question
If 
is a root of 
, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
B)
C)
D)
E)
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
B)
C)
D)
E)
Question
Find all zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Given 
is a root, determine all other roots of 
.
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
Question
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find all real solutions of the polynomial equation 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find all the rational zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Question
Given 
is a root, determine all other roots of 
.
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
Question
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
Question
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
Question
Find all the rational zeros of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
After determining whether the variation model below is of the form 
or 
, find the value of k.
A)
B)
C)
D)
E)
or , find the value of k.A)
B)
C)
D)
E)
Question
Determine whether the variation model below is of the form 
or 
.
A)
B)
or .A)
B)
Question
After determining whether the variation model below is of the form 
or 
, find the value of k.
A)
B)
C)
D)
E)
or , find the value of k.A)
B)
C)
D)
E)
Question
Find a mathematical model for the verbal statement: "z varies directly as the square of x and inversely as p."
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of 
.
A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 3 positive reals or 1 positive real; 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) 3 positive reals or 1 positive real; no negative reals
.A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 3 positive reals or 1 positive real; 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) 3 positive reals or 1 positive real; no negative reals
Question
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Assume that y is directly proportional to x. If 
and 
, determine a linear model that relates y and x.
A)
B)
C)
D)
E)
and , determine a linear model that relates y and x.A)
B)
C)
D)
E)
Question
Find a mathematical model for the verbal statement: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of 
.
A) 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
.A) 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
Question
Hooke's law states that the magnitude of force, F, required to stretch a spring x units beyond its natural length is directly proportional to x. If a force of 2 pounds stretches a spring from its natural length of 10 inches to a length of 10.7 inches, what force will stretch the spring to a length of 11.5 inches? Round answer to nearest hundredth.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all the real zeros of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Question
The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 100 meters long of diameter 5 millimeters has a resistance of 8 ohms. Find the resistance of a wire made of the same material that has a diameter of 4 millimeters and is 64 meters long.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of 
.
A) no positive reals; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 0 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
.A) no positive reals; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 0 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
Question
Determine whether the variation model below is of the form 
or 
.
A)
B)
or .A)
B)
Question
The simple interest on an investment is directly proportional to the amount of the investment. By investing $7750 in a certain certificate of deposit, you obtained an interest payment of $372.00 after 1 year. Determine a mathematical model that gives the interest, I , for this CD after 1 year in terms of the amount invested, P.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 4: Polynomial Functions
1
Determine the vertex of the graph of the quadratic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
2
From the graph of the quadratic function , determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
3
Write the quadratic function in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
4
Write the standard form of the equation of the parabola that has a vertex at and passes through the point .
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
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5
Write the standard form of the equation of the parabola that has a vertex at and passes through the point .
A)
B)
C)
D)
E)
and passes through the point .A)
B)
C)
D)
E)
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6
Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 280.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Compare the graph of with .
A) shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9.
B) shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9.
C) shifts right 7 units, shifts downward 5 units, and shrinks by a factor of
)
D) shifts right 7 units, shifts upward 5 units, and shrinks by a factor of
)
E) shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9.
with .A)
shifts left 7 units, shifts downward 5 units, and stretches by a factor of 9.B)
shifts left 7 units, shifts upward 5 units, and stretches by a factor of 9.C)
shifts right 7 units, shifts downward 5 units, and shrinks by a factor of )
D)
shifts right 7 units, shifts upward 5 units, and shrinks by a factor of )
E)
shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9. Unlock Deck
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8
Describe the right-hand and the left-hand behavior of the graph of .
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
.A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
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9
Find two positive real numbers whose product is a maximum and whose sum is 156.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
The height, , of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?
A)
B)
C)
D)
E)
, of a punted rugby ball is given by where x is the horizontal distance in feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point?A)
B)
C)
D)
E)
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11
From the graph of the quadratic function , determine the equation of the axis of symmetry.
A)
B)
C)
D)
E)
, determine the equation of the axis of symmetry.A)
B)
C)
D)
E)
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12
A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Write the quadratic function in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
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14
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Compare the graph of with .
A) - 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of
)
B) - 8 shifts right 4 units, shifts upward 8 units, and shrinks by a factor of
)
C) - 8 shifts left 16 units, shifts upward 8 units, and shrinks by a factor of
)
D) - 8 shifts right 16 units, shifts upward 8 units, and shrinks by a factor of
)
E) - 8 shifts right 4 units, shifts downward 8 units, and shrinks by a factor of
)
with .A)
- 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of )
B)
- 8 shifts right 4 units, shifts upward 8 units, and shrinks by a factor of )
C)
- 8 shifts left 16 units, shifts upward 8 units, and shrinks by a factor of )
D)
- 8 shifts right 16 units, shifts upward 8 units, and shrinks by a factor of )
E)
- 8 shifts right 4 units, shifts downward 8 units, and shrinks by a factor of )
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16
Determine the x-intercept(s) of the quadratic function .
A)
B)
C)
D)
E) no x-intercept(s)
.A)
B)
C)
D)
E) no x-intercept(s)
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17
Determine the x-intercept(s) of the quadratic function .
A)
B)
C) no x-intercept(s)
D)
E)
.A)
B)
C) no x-intercept(s)
D)
E)
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18
Write the quadratic function in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
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19
A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is , express the area, A, as a function of the width, x, of the window.
A)
B)
C)
D)
E)
, express the area, A, as a function of the width, x, of the window. A)
B)
C)
D)
E)
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20
Find the standard form of the quadratic function shown below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 76 flashcards in this deck.
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23
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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24
Use synthetic division to divide.
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25
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
Using a graphing utility, graph and approximate the zeros and their multiplicity.
A)
B)
C)
D)
E)
and approximate the zeros and their multiplicity.A)
B)
C)
D)
E)
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27
Write in the form when .
A)
B)
C)
D)
E)
in the form when .A)
B)
C)
D)
E)
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k this deck
28
Find all real zeros of the polynomial and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
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29
If , use synthetic division to evaluate .
A)
B)
C)
D)
E)
, use synthetic division to evaluate .A)
B)
C)
D)
E)
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30
An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by , determine the domain of .
A)
B)
C)
D)
E)
, determine the domain of . A)
B)
C)
D)
E)
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31
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
32
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
33
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Unlock Deck
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34
Find all real zeros of the polynomial and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
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35
Describe the right-hand and the left-hand behavior of the graph of .
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
.A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
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36
Find all real zeros of the polynomial and determine the multiplicity of each.
A)
B)
C)
D)
E)
and determine the multiplicity of each.A)
B)
C)
D)
E)
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k this deck
37
Describe the right-hand and the left-hand behavior of the graph of .
A) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
.A) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
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38
An open box is to be made from a square piece of cardboard, 21 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Write in the form when , and demonstrate that .
in the form when , and demonstrate that . Unlock Deck
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40
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 76 flashcards in this deck.
Unlock Deck
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41
Find all zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
42
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
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43
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
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44
Find all zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock Deck
k this deck
45
Use the zero or root feature of a graphing utility to approximate the zeros of accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
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46
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A) ;
B) ;
C) ;
D) ;
E) ;
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
; B)
; C)
; D)
; E)
; Unlock Deck
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47
Given is a root, determine all other roots of .
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
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k this deck
48
Use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to the nearest thousandth.
A)
B)
C)
D)
E)
accurate to the nearest thousandth.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 76 flashcards in this deck.
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k this deck
49
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
50
If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.
A)
B)
C)
D)
E)
is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.A)
B)
C)
D)
E)
Unlock Deck
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51
Find all zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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52
Given is a root, determine all other roots of .
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
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53
Find all real solutions of the polynomial equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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54
Find all real solutions of the polynomial equation .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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55
Find all the rational zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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56
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
57
Given is a root, determine all other roots of .
A)
B)
C)
D)
E)
is a root, determine all other roots of .A)
B)
C)
D)
E)
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k this deck
58
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
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k this deck
59
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
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k this deck
60
Find all the rational zeros of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
61
After determining whether the variation model below is of the form or , find the value of k.
A)
B)
C)
D)
E)
or , find the value of k.A)
B)
C)
D)
E)
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62
Determine whether the variation model below is of the form or .
A)
B)
or .A)
B)
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63
After determining whether the variation model below is of the form or , find the value of k.
A)
B)
C)
D)
E)
or , find the value of k.A)
B)
C)
D)
E)
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64
Find a mathematical model for the verbal statement: "z varies directly as the square of x and inversely as p."
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .
A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 3 positive reals or 1 positive real; 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) 3 positive reals or 1 positive real; no negative reals
.A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 3 positive reals or 1 positive real; 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) 3 positive reals or 1 positive real; no negative reals
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66
Find all the real zeros of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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67
Assume that y is directly proportional to x. If and , determine a linear model that relates y and x.
A)
B)
C)
D)
E)
and , determine a linear model that relates y and x.A)
B)
C)
D)
E)
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68
Find a mathematical model for the verbal statement:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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69
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .
A) 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
.A) 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
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70
Hooke's law states that the magnitude of force, F, required to stretch a spring x units beyond its natural length is directly proportional to x. If a force of 2 pounds stretches a spring from its natural length of 10 inches to a length of 10.7 inches, what force will stretch the spring to a length of 11.5 inches? Round answer to nearest hundredth.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Find all the real zeros of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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72
The sales tax on an item with a retail price of $972 is $77.76. Create a variational model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $92.34.
A) $1156.24
B) $1125.88
C) $1154.25
D) $1166.48
E) $1098.56
A) $1156.24
B) $1125.88
C) $1154.25
D) $1166.48
E) $1098.56
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73
The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 100 meters long of diameter 5 millimeters has a resistance of 8 ohms. Find the resistance of a wire made of the same material that has a diameter of 4 millimeters and is 64 meters long.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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74
Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .
A) no positive reals; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 0 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
.A) no positive reals; no negative reals
B) 1 positive real; 3 negative reals or 1 negative real
C) 0 positive real; 3 negative reals or 1 negative real
D) 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
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75
Determine whether the variation model below is of the form or .
A)
B)
or .A)
B)
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76
The simple interest on an investment is directly proportional to the amount of the investment. By investing $7750 in a certain certificate of deposit, you obtained an interest payment of $372.00 after 1 year. Determine a mathematical model that gives the interest, I , for this CD after 1 year in terms of the amount invested, P.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
Unlock for access to all 76 flashcards in this deck.
