Question 1

Solve the problem.
-A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 344 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the problem.
-A developer wants to enclose...

Question 2

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express the function in the form f(x)...

Question 3

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry.
-
A) 
B) 
C) 
D)

Accepted Answer

The vertex is (-2,4), the x-intercepts are (-4,0) and (0,0), and the equation for the axis of symmetry is x = -2. Choice C corresponds to this graph. The vertex is (-1, 4). There is only one x-intercept at (-2, 0). The axis of symmetry is x = -1. 
Choice C correctly represents these properties on the graph.

Question 4

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
-
A) f(x) = -(x + 14)2 + 3
B)  vertex: (-14, 3)
C) 
D)

Accepted Answer

The answer of Express the function in the form f(x)...

Question 5

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function. Identify the vertex, x-intercepts,...

Question 6

Match the graph with the appropriate function.
-
A) 
B) 
C) 
D)

Accepted Answer

The graph is a straight line passing through the origin, which means it is a linear function. The equation of the line can be written in slope-intercept form as y = mx, where m is the slope. The slope of the line in the graph is 3, so the equation of the line is y = 3x.

Question 7

Solve the problem.
-The profit that a vendor makes per day by selling x pretzels is given by the function  Find the number of pretzels that must be sold to maximize profit.
A) 300 pretzels
B) 600 pretzels
C) 30 pretzels
D) 0.6 pretzels

Accepted Answer

The answer of Solve the problem.
-The profit that a vendor...

Question 8

Solve the problem.
-The length and width of a rectangle must have a sum of 104 feet. Find the dimensions of the rectangle whose area is as large as possible.
A) 
B) l = 52 ft; w = 156 ft
C) l = 52 ft; w = 52 ft
D) l = 51 ft; w = 53 ft

Accepted Answer

The answer of Solve the problem.
-The length and width of...

Question 9

Solve the problem.
-An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function  Find the maximum height of the
Arrow.
A) 144 ft
B) 432 ft
C) 48 ft
D) 240 ft

Accepted Answer

The answer of Solve the problem.
-An arrow is fired into...

Question 10

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
-
A) 
B) 
C) 
D)

Accepted Answer

The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex. Looking at the graph, we can see that the vertex is at (-2, 3). We can then write the function as:
f(x) = a(x + 2)2 + 3
Now we need to find the value of a. We can use one of the other points on the graph to solve for a. Let's use the point (0, 7):
7 = a(0 + 2)2 + 3
7 = 4a + 3
4a = 4
a = 1
Therefore, the function is:
f(x) = (x + 2)2 + 3
And the vertex is at (-2, 3). 
The correct choice based on this explanation is A.

Question 11

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
-
A) 
B) 
C) 
D)

Accepted Answer

By completing the square, we can rewrite the given quadratic function as f(x) = 2(x + 3)2 - 5. This is in the form f(x) = a(x - h)2 + k, where a = 2, h = -3, and k = -5. The vertex of the parabola is at the point (-3, -5). Therefore, the correct choice is B. To express the function in the form f(x) = a(x - h)2 + k, we need to complete the square. We have: f(x) = 3x2 - 6x + 4. To complete the square, we first factor out the 3: f(x) = 3(x2 - 2x) + 4. To find the constant term we need to add inside the parentheses, we take half of the coefficient of the x-term and square it: (2/2)2 = 1. So we add 1 inside the parentheses and compensate by subtracting 3 from the overall expression: f(x) = 3(x - 1)2 + 1. Therefore, the vertex is at (1,1).

Question 12

Solve the problem.
-A person is standing on the top of a building 50 feet above the ground. They project an object upward with an initial velocity of 40 feet per second. The object's distance above the ground, d, after t seconds may be found by
The formula  What is the maximum height the object will reach. How much time does it take
To fall back to the ground? Assume that it takes the same time for going up and coming down.
A) maximum height = 75 ft; time to reach ground = 1.25 seconds
B) maximum height = 50 ft; time to reach ground = 1.25 seconds
C) maximum height = 50 ft; time to reach ground = 2.5 seconds
D) maximum height = 75 ft; time to reach ground = 2.5 seconds

Accepted Answer

The answer of Solve the problem.
-A person is standing on...

Question 13

Solve the problem.
-A projectile is fired from a cliff 200 feet above the water at an inclination of 45° to the horizontal, with an initial velocity of 180 feet per second. The height h of the projectile above the water is given by  where x is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the
Projectile.
A) 506.25 ft
B) 453.13 ft
C) 959.38 ft
D) 253.13 ft

Accepted Answer

The answer of Solve the problem.
-A projectile is fired from...

Question 14

Match the graph with the appropriate function.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the graph with the appropriate function.
-
A)...

Question 15

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function. Identify the vertex, x-intercepts,...

Question 16

Express the function in the form f(x) = a(x - h)2 + k and indicate the vertex.
-
A) 
B) 
C) 
D)

Accepted Answer

The vertex form of the quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex. From the given graph, we can see that the vertex is at (-2, 3). To find the value of a, we can use another point on the graph, such as (0, -1). Plugging in these values, we get -1 = a(0 - (-2))2 + 3, which simplifies to -1 = 4a + 3. Solving for a, we get a = -1. Plugging this value into the vertex form, we get f(x) = -1(x + 2)2 + 3, which matches choice C.

Question 17

Solve the problem.
-The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 4x2 - 16x + 32. Find the number of automobiles that must be produced to minimize the cost.
A) 16 thousand automobiles
B) 4 thousand automobiles
C) 2 thousand automobiles
D) 8 thousand automobiles

Accepted Answer

The function C(x) = 4x^2 - 16x + 32 is a quadratic function that opens upwards (since the coefficient of x^2 is positive). The minimum cost occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/(2a), where a = 4 and b = -16. Thus, x = -(-16)/(2*4) = 2. Therefore, 2 thousand automobiles must be produced to minimize the cost.

Question 18

Match the graph with the appropriate function.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the graph with the appropriate function.
-
A)...

Question 19

Match the graph with the appropriate function.
-
A) 
B) 
C) 
D)

Accepted Answer

The graph shows a periodic wave with a maxima at x=0 and a minima at x=π. This matches the sine function, which has an amplitude of 2, a period of 2π, and a phase shift of 0. The only function that matches this description is choice B, which is y=2sin(x). The graph appears to be a straight line with a positive slope. The only function that matches this description is y = x + 2, which is represented by graph B.

Question 20

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the function. Identify the vertex, x-intercepts,...

Quiz 12: Quadratic Functions

Solve the problem. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 344 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. -

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry. -

Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. -

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry. -

Match the graph with the appropriate function. -

Solve the problem. -The profit that a vendor makes per day by selling x pretzels is given by the function Find the number of pretzels that must be sold to maximize profit.

Solve the problem. -The length and width of a rectangle must have a sum of 104 feet. Find the dimensions of the rectangle whose area is as large as possible.

Solve the problem. -An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function Find the maximum height of the Arrow.

Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. -

Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. -

Match the graph with the appropriate function. -

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry. -

Express the function in the form f(x) = a(x - h) 2 + k and indicate the vertex. -

Solve the problem. -The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 4x2 - 16x + 32. Find the number of automobiles that must be produced to minimize the cost.

Match the graph with the appropriate function. -

Match the graph with the appropriate function. -

Graph the function. Identify the vertex, x-intercepts, and the equation for the axis of symmetry. -