Question 1

Find the vertex of the parabola.
-$$f ( x ) = x ^ { 2 } + 16 x - 8$$
A) $\left( - 8 , \frac { 11 } { 4 } \right)$
B) $( 16 , - 8 )$
C) $( - 8 , - 72 )$
D) $( - 16,8 )$

Accepted Answer

The vertex of a parabola in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. For the given equation, $a = 1$, $b = 16$, and $c = -8$. Thus, the x-coordinate of the vertex is $- \frac{16}{2(1)} = -8$. Substituting $x = -8$ into the original equation gives $f(-8) = (-8)^2 + 16(-8) - 8 = 64 - 128 - 8 = -72$. Therefore, the vertex is $(-8, -72)$.

Question 2

Find the vertex of the parabola.
-$$q ( x ) = 2 x ^ { 2 } - 12 x - 1$$
A) $( 3 , - 31 )$
B) $( - 3 , - 19 )$
C) $( - 3 , - 31 )$
D) $( 3 , - 19 )$

Accepted Answer

D

Question 3

Graph the function.
-$$h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6$$
A)

B)

C)

D)

Accepted Answer

A

Question 4

Choose the one alternative that best completes the statement or answers the question.
Determine whether the graph of the parabola opens upward or downward and determine the range.
-$$f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2$$
A) Downward
Range: $( - \infty , - 2 ]$

B) Upward
Range: $[ - 2 , \infty )$

C) Upward
Range: $[ 2 , \infty )$

D) Downward
Range: $( - \infty , 2 ]$

Accepted Answer

The coefficient of the squared term is negative (-3), indicating the parabola opens downward. The vertex form of the parabola shows the vertex at (2, -2), making the highest point of the parabola -2. Therefore, the range is all real numbers less than or equal to -2.

Question 5

Find the vertex.
-$$p ( x ) = - \frac { 1 } { 7 } ( x + 8 ) ^ { 2 } + 1$$
A) $( 8 , - 1 )$
B) $( 8,1 )$
C) $( - 8 , - 1 )$
D) $( - 8,1 )$

Accepted Answer

The vertex form of a parabola is $p(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. In the given equation, $p(x) = -\frac{1}{7}(x + 8)^2 + 1$, the vertex is $(-8, 1)$ because it matches the form with $h = -8$ and $k = 1$.

Question 6

Determine the x- and y-intercepts for the given function.
-$$f ( x ) = - ( x - 2 ) ^ { 2 } - 4$$
A) $x$-intercepts: $( 0,0 )$ and $( 4,0 )$
$y$-intercept: $( 0 , - 8 )$

B) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0 , - 4 )$

C) $x$-intercept: none
$y$-intercept: $( 0 , - 8 )$

D) $x$-intercept: $( 2,0 )$
$y$-intercept: $( 0,4 )$

Accepted Answer

The function is a downward-opening parabola with vertex at (2, -4). It does not cross the x-axis, so there are no x-intercepts. The y-intercept is found by setting x = 0, giving y = -8.

Question 7

Sketch the function and determine the axis of symmetry.
-$$f ( x ) = 3 ( x - 1 ) ^ { 2 } + 6$$
A) Axis of symmetry: $x = - 1$

B) Axis of symmetry: $x = - 6$

C) Axis of symmetry: $x = 6$

D) Axis of symmetry: $x = 1$

Accepted Answer

The answer of Sketch the function and determine the axis...

Question 8

Graph the function and determine the minimum or maximum value of the function.
-$$m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$$
A) minimum value $= 0$

B) maximum value $= 0$

C) maximum value $= 0$

D) minimum value $= 0$

Accepted Answer

The answer of Graph the function and determine the minimum...

Question 9

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Accepted Answer

The answer of Given \(f ( x ) = a...

Question 10

Identify the graph of the function.
-$$h ( x ) = ( x + 1 ) ^ { 2 } - 2$$
A)

B)

C)

D)

Accepted Answer

The answer of Identify the graph of the function.
-\[h (...

Question 11

Identify the vertex and determine the minimum or maximum value of the function.
-$$f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$$
A) Vertex: $( 4,7 )$
Maximum: 7

B) Vertex: $( 4,7 )$
Minimum: 7

C) Vertex: $( 4 , - 7 )$
Minimum: -7

D) Vertex: $( 4 , - 7 )$
Maximum: -7

Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function, $h = 4$ and $k = 7$, so the vertex is $(4, 7)$. Since $a = -2$ is negative, the parabola opens downwards, indicating a maximum value at the vertex. Thus, the maximum value is 7.

Question 12

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

Accepted Answer

The answer of Given \(f ( x ) = a...

Question 13

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

Accepted Answer

The answer of The vertical line drawn through the vertex...

Question 14

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.

Accepted Answer

The answer of A function defined by \(f ( x...

Question 15

Find the vertex of the parabola.
-$$h ( x ) = - 2 x ^ { 2 } + 12 x - 19$$
A) $( - 3 , - 1 )$
B) $( - 1 , - 3 )$
C) $( 0 , - 19 )$
D) $( 3 , - 1 )$

Accepted Answer

The vertex of a parabola in the form $h(x) = ax^2 + bx + c$ can be found using the formula $(-\frac{b}{2a}, h(-\frac{b}{2a}))$. For $h(x) = -2x^2 + 12x - 19$, $a = -2$, $b = 12$, so the x-coordinate of the vertex is $-\frac{12}{2(-2)} = 3$. Plugging $x = 3$ back into the equation gives $h(3) = -2(3)^2 + 12(3) - 19 = -18 + 36 - 19 = -1$. Therefore, the vertex is $(3, -1)$.

Question 16

Find the vertex.
-$$f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$$
A) $( 13 , - 19 )$
B) $( 13,19 )$
C) $( - 19,13 )$
D) $( 19,13 )$

Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. In the given function, $h = 19$ and $k = 13$, making the vertex $(19, 13)$.

Question 17

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the
equation of the axis of symmetry.
-$$y = - ( x - 5 ) ^ { 2 } + 2$$
A)

Vertex $( - 5 , - 2 )$
axis of symmetry: $x = - 5$

B)
Vertex $( - 5,2 )$
axis of symmetry: $x = - 5$

C)

Vertex $( 5 , - 2 )$
axis of symmetry: $x = 5$

D)

Vertex $( 5,2 )$
axis of symmetry: $x = 5$

Accepted Answer

The answer of Graph the parabola and the axis of...

Question 18

$\text { The graph of } f ( x ) = a ( x - h ) ^ { 2 } + k , a \neq 0$ 0, is a parabola and the axis of symmetry is a line given by________

Accepted Answer

The answer of \(\text { The graph of } f...

Question 19

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a > 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is________ .

Accepted Answer

The answer of Given \(f ( x ) = a...

Question 20

Graph the function.
-$$g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$$
A)

B)

C)

D)

Accepted Answer

The answer of Graph the function.
-\[g ( x ) =...

Quiz 3: Polynomial and Rational Functions

Find the vertex of the parabola. - $f ( x ) = x ^ { 2 } + 16 x - 8$

Find the vertex of the parabola. - $q ( x ) = 2 x ^ { 2 } - 12 x - 1$

Graph the function. - $h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6$

Choose the one alternative that best completes the statement or answers the question. Determine whether the graph of the parabola opens upward or downward and determine the range. - $f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2$

Find the vertex. - $p ( x ) = - \frac { 1 } { 7 } ( x + 8 ) ^ { 2 } + 1$

Determine the x- and y-intercepts for the given function. - $f ( x ) = - ( x - 2 ) ^ { 2 } - 4$

Sketch the function and determine the axis of symmetry. - $f ( x ) = 3 ( x - 1 ) ^ { 2 } + 6$

Graph the function and determine the minimum or maximum value of the function. - $m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Identify the graph of the function. - $h ( x ) = ( x + 1 ) ^ { 2 } - 2$

Identify the vertex and determine the minimum or maximum value of the function. - $f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.

Find the vertex of the parabola. - $h ( x ) = - 2 x ^ { 2 } + 12 x - 19$

Find the vertex. - $f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - $y = - ( x - 5 ) ^ { 2 } + 2$

$\text { The graph of } f ( x ) = a ( x - h ) ^ { 2 } + k , a \neq 0$ 0, is a parabola and the axis of symmetry is a line given by________

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a > 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is________ .

Graph the function. - $g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$

Quiz 3: Polynomial and Rational Functions

Find the vertex of the parabola. - f(x) =x2+16x−8f ( x ) = x ^ { 2 } + 16 x - 8f(x) =x2+16x−8

Find the vertex of the parabola. - q(x) =2x2−12x−1q ( x ) = 2 x ^ { 2 } - 12 x - 1q(x) =2x2−12x−1

Graph the function. - h(x) =−13(x−3) 2+6h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6h(x) =−31​(x−3) 2+6

Choose the one alternative that best completes the statement or answers the question. Determine whether the graph of the parabola opens upward or downward and determine the range. - f(x) =−3(x−2) 2−2f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2f(x) =−3(x−2) 2−2

Find the vertex. - p(x) =−17(x+8) 2+1p ( x ) = - \frac { 1 } { 7 } ( x + 8 ) ^ { 2 } + 1p(x) =−71​(x+8) 2+1

Determine the x- and y-intercepts for the given function. - f(x) =−(x−2) 2−4f ( x ) = - ( x - 2 ) ^ { 2 } - 4f(x) =−(x−2) 2−4

Sketch the function and determine the axis of symmetry. - f(x) =3(x−1) 2+6f ( x ) = 3 ( x - 1 ) ^ { 2 } + 6f(x) =3(x−1) 2+6

Graph the function and determine the minimum or maximum value of the function. - m(x) =−14(x+1) 2m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }m(x) =−41​(x+1) 2

Given f(x)=a(x−h)2+k, if a<0f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0f(x)=a(x−h)2+k, if a<0 e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Identify the graph of the function. - h(x) =(x+1) 2−2h ( x ) = ( x + 1 ) ^ { 2 } - 2h(x) =(x+1) 2−2

Identify the vertex and determine the minimum or maximum value of the function. - f(x) =−2(x−4) 2+7f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7f(x) =−2(x−4) 2+7

Given f(x)=a(x−h)2+k(a≠0)f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )f(x)=a(x−h)2+k(a=0) he vertex of the parabola is the point ________.

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

A function defined by f(x)=ax2+bx+c(a≠0)f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )f(x)=ax2+bx+c(a=0) 0) is called a________ function.

Find the vertex of the parabola. - h(x) =−2x2+12x−19h ( x ) = - 2 x ^ { 2 } + 12 x - 19h(x) =−2x2+12x−19

Find the vertex. - f(x) =−2(x−19) 2+13f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13f(x) =−2(x−19) 2+13

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - y=−(x−5) 2+2y = - ( x - 5 ) ^ { 2 } + 2y=−(x−5) 2+2

The graph of f(x)=a(x−h)2+k,a≠0\text { The graph of } f ( x ) = a ( x - h ) ^ { 2 } + k , a \neq 0 The graph of f(x)=a(x−h)2+k,a=0 0, is a parabola and the axis of symmetry is a line given by________

Given f(x)=a(x−h)2+k, if a>0f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a > 0f(x)=a(x−h)2+k, if a>0 e parabola opened (upward/downward) and the (minimum/maximum) value is________ .

Graph the function. - g(x) =−12(x−1) 2+2g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2g(x) =−21​(x−1) 2+2

Find the vertex of the parabola. - $f ( x ) = x ^ { 2 } + 16 x - 8$

Find the vertex of the parabola. - $q ( x ) = 2 x ^ { 2 } - 12 x - 1$

Graph the function. - $h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6$

Choose the one alternative that best completes the statement or answers the question. Determine whether the graph of the parabola opens upward or downward and determine the range. - $f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2$

Find the vertex. - $p ( x ) = - \frac { 1 } { 7 } ( x + 8 ) ^ { 2 } + 1$

Determine the x- and y-intercepts for the given function. - $f ( x ) = - ( x - 2 ) ^ { 2 } - 4$

Sketch the function and determine the axis of symmetry. - $f ( x ) = 3 ( x - 1 ) ^ { 2 } + 6$

Graph the function and determine the minimum or maximum value of the function. - $m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Identify the graph of the function. - $h ( x ) = ( x + 1 ) ^ { 2 } - 2$

Identify the vertex and determine the minimum or maximum value of the function. - $f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.

Find the vertex of the parabola. - $h ( x ) = - 2 x ^ { 2 } + 12 x - 19$

Find the vertex. - $f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the equation of the axis of symmetry. - $y = - ( x - 5 ) ^ { 2 } + 2$

$\text { The graph of } f ( x ) = a ( x - h ) ^ { 2 } + k , a \neq 0$ 0, is a parabola and the axis of symmetry is a line given by________

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a > 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is________ .

Graph the function. - $g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$