Question 1

In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 500 m apart and the lowest point of the suspension cables is 120 m below the top of the towers as shown below. Find a quadratic function that models the parabolic part of the cables placing the origin of the coordinate axes at the vertex. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of In a suspension bridge the shape of...

Question 2

Find the maximum or minimum value of the quadratic function  .
A) The maximum value is  .
B) The maximum value is  .
C) The minimum value is 7.
D) The minimum value is  .
E) The minimum value is  .

Accepted Answer

The answer of Find the maximum or minimum value of...

Question 3

Find the minimum value and the corresponding x -value at which the minimum occurs for the function  .
A) Minimum value of 5 occurs when 
B) Minimum value of  occurs when  
C) Minimum value of  occurs when  
D) Minimum value of 1 occurs when 
E) Minimum value of 1 occurs when

Accepted Answer

The answer of Find the minimum value and the corresponding...

Question 4

Find the vertex of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the vertex of  .
A) 
B)...

Question 5

Given the function  find the average rate of change between  and  .
A) 0.05
B) 21
C) 7
D) 147
E) -3

Accepted Answer

The answer of Given the function  find the average...

Question 6

Using the graph below find the y -value at which the minimum value of the function occurs. 
A)  
B)  
C) 
D)  2
E)

Accepted Answer

The minimum value of the function occurs at the vertex of the parabola. The vertex is located at the point with the x-coordinate equal to the axis of symmetry, which is given by x = -b/2a. In this case, the axis of symmetry is x = 2, so we need to find the y-coordinate of the point on the graph where x = 2. We can see that this point lies on the curve labeled "f(x)", and we can read off the y-coordinate from the vertical axis. The y-coordinate appears to be approximately -2.5. The only choice that matches this value is B.

Question 7

If  represents Mark s driving distance (in miles) after t minutes on the road which one of the following would describe the meaning of  ?
A) Not enough information.
B) Mark's driving distance plus an additional 5 miles.
C) Mark's driving distance after traveling for 5 minutes.
D) Mark s driving distance while traveling  miles per minute.
E) Mark s time driving on the road is  minutes.

Accepted Answer

The answer of If  represents Mark s driving distance...

Question 8

Find a quadratic function g whose graph is shown below. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a quadratic function g whose graph...

Question 9

Using the graph below find the y -value at which the maximum value of the function occurs. 
A)  7
B)  2
C)  
D)  
E)  2

Accepted Answer

The answer of Using the graph below find the y...

Question 10

A function f is given by the table. Find when 
A) 5
B) -4
C) 8
D) 0
E) -2

Accepted Answer

The answer of A function f is given by the...

Question 11

Express  in the standard form of a quadratic function.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Express  in the standard form of...

Question 12

Express  in the general form of a quadratic function.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Express  in the general form of...

Question 13

Using the graph below find the x -value at which the minimum value of the function occurs. 
A) 
B)  
C)  
D) 
E)

Accepted Answer

The x-value at which the minimum value of the function occurs is where the graph reaches its lowest point, which is at the bottom of the dip in the graph. This occurs at the x-value of approximately -3. Therefore, the best choice is B.

Question 14

Which one of the following functions describes a function f whose graph is a parabola with the vertex  and passes through the point  ?
A) 
B) 
C) 
D) f(x) =  
E) f(x) =

Accepted Answer

The answer of Which one of the following functions describes...

Question 15

If  represents John s salary per month (in thousands of dollars) after working  number of months at a certain job which one of the following would describe the meaning of  ?
A) John s salary after working  months at the job.
B) John's raise of $3 per month.
C) John's salary after working 3 months at the job.
D) Not enough information.
E) John's total number of months working at the job.

Accepted Answer

The string of characters before the last underscore represents a unique identifier for John's salary per month after working a certain number of months. Therefore, the only description that can be inferred from the given string is John's salary after working a specific number of months, in this case, represented by "11ec19db_84d4_98c2_9dbe_9b0af5808f81".

Question 16

The graph of g is given below and represents a translation of the graph of  . Which one of the functions best describes the graph of g . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The graph of g appears to be a translation of the graph of f(x) = |x| down 2 units and to the right 1 unit. The function that corresponds to this translation is g(x) = |x - 1| - 2, which is choice B.

Question 17

Find the vertex of  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the vertex of  .
A) 
B)...

Question 18

Using the graph below find the x -value at which the maximum value of the function occurs. 
A)  
B)  
C) 
D) 
E)

Accepted Answer

The answer of Using the graph below find the x...

Question 19

The graph of g is given below and represents a transformation of the graph of  . Which one of the functions best describes the graph of g . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The graph of g is given below...

Question 20

Express  in the standard form of a quadratic function.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Express  in the standard form of...

Quiz 5: Exponents and Polynomials

Find the maximum or minimum value of the quadratic function .

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

Find the vertex of .

Given the function find the average rate of change between and .

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

If represents Mark s driving distance (in miles) after t minutes on the road which one of the following would describe the meaning of ?

Find a quadratic function g whose graph is shown below.

Using the graph below find the y -value at which the maximum value of the function occurs.

A function f is given by the table. Find when

Express in the standard form of a quadratic function.

Express in the general form of a quadratic function.

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

Which one of the following functions describes a function f whose graph is a parabola with the vertex and passes through the point ?

If represents John s salary per month (in thousands of dollars) after working number of months at a certain job which one of the following would describe the meaning of ?

The graph of g is given below and represents a translation of the graph of . Which one of the functions best describes the graph of g .

Find the vertex of .

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

The graph of g is given below and represents a transformation of the graph of . Which one of the functions best describes the graph of g .

Express in the standard form of a quadratic function.