Question 1

Find the vertex of  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

The number of oranges produced by each tree in an orange grove depends on how densely the trees are planted. If n trees are planted on an acre of land, then each tree produces  oranges. So the number of oranges produced per acre is  What is the maximum yield of the trees, and how many trees should be planted per acre to obtain the maximum yield of oranges? (Rounded to the nearest whole number)

Accepted Answer

A)  Maximum yield of the trees is 625 oranges when 9 trees are planted 
B)  Maximum yield of the trees is 10,851 oranges when 35 trees are planted 
C)  There is no maximum yield of the trees 
D)  Maximum yield of the trees is 7,350 oranges when 15 trees are planted 
E)  Maximum yield of the trees is 27,500 oranges when 100 trees are planted

Question 3

Using the graph below, find the x -value at which the minimum value of the function occurs.

Accepted Answer

A)   
B)    
C)    
D)   
E)

Question 4

A function f is given by the table. Find when .

Accepted Answer

A)  5 
B)  -4 
C)  8 
D)  0 
E)  -2

Question 5

A function f is given by the table. Find .

Accepted Answer

A)  3 
B)  -1 
C)  4 
D)  -4 
E)  0

Question 6

Express  in the general form of a quadratic function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

The quadratic function  has a maximum value at  .

Accepted Answer

A) True 
 B)False

Question 8

Find the maximum value and the corresponding x -value at which the maximum occurs for the function  .

Accepted Answer

A)  Maximum value of 12 occurs when  
B)  Maximum value of 28 occurs when  12 
C)  Maximum value of 4 occurs when  0 
D)  Maximum value of 12 occurs when  28 
E)  Maximum value of 28 occurs when

Question 9

Express  in the standard form of a quadratic function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Solve the equation  by factoring.

Accepted Answer

A)   and  
B)   and  
C)   and  
D)   and  
E)   and

Question 11

Which one of the following is the graph for the function  ?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Solve the equation  using the Quadratic Formula.

Accepted Answer

A)   
B)   
C)   
D)   
E)   and

Question 13

A rectangular parking lot is 20 feet longer than it is wide. Which one of the following functions model the area of the lot?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Solve the equation  using the Quadratic Formula. Round answers to nearest hundredth.

Accepted Answer

A)   and  
B)  No real solutions 
C)   and  
D)   and  
E)   and

Question 15

The quadratic function  has a maximum value at  when  .

Accepted Answer

A) True 
 B)False

Question 16

The equation  has 2 real solutions.

Accepted Answer

A) True 
 B)False

Question 17

Express  in the general form of a quadratic function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

The vertex of  is  .

Accepted Answer

A) True 
 B)False

Question 19

The following table shows the values of the number of gallons of water used by a family during the month of July.

Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)

Accepted Answer

A)   
B)  Not enough information. 
C)   
D)   
E)

Question 20

A diver jumps off the springboard and dives into a pool. The following table shows the distance of the diver from the surface of the water as a function of the time (in seconds) it takes for the diver to enter the water of the pool.

Based on a quadratic regression model, when will the diver enter the water? (Rounded to the nearest tenth)

Accepted Answer

A)  After 2.8 seconds 
B)  After 2.6 seconds 
C)  After 2.9 seconds 
D)  After 2.7 seconds 
E)  After 3.0 seconds

Exam 5: Quadratic Functions and Models

Find the vertex of .

Using the graph below, find the x -value at which the minimum value of the function occurs.

A function f is given by the table. Find when .

A function f is given by the table. Find .

Express in the general form of a quadratic function.

The quadratic function has a maximum value at .

Find the maximum value and the corresponding x -value at which the maximum occurs for the function .

Express in the standard form of a quadratic function.

Solve the equation by factoring.

Which one of the following is the graph for the function ?

Solve the equation using the Quadratic Formula.

A rectangular parking lot is 20 feet longer than it is wide. Which one of the following functions model the area of the lot?

Solve the equation using the Quadratic Formula. Round answers to nearest hundredth.

The quadratic function has a maximum value at when .

The equation has 2 real solutions.

Express in the general form of a quadratic function.

The vertex of is .

The following table shows the values of the number of gallons of water used by a family during the month of July. Find the quadratic model based on the data provided that determines the number of gallons of water used as a function of the day. (Rounded to the nearest hundredth)