Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

The minimum value of the function occurs at the lowest point on the graph, which is at the lowest point of the parabola. This point has an x-coordinate of approximately -3. Therefore, the x-value at which the minimum value of the function occurs is approximately -3, which is closest to the x-coordinate of point B (-2.9).

Question 4

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.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find the vertex of  .

Accepted Answer

The answer of Find the vertex of  .
...

Question 8

Express  in the standard form of a quadratic function.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Express  in the general form of a quadratic function.

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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  ?

Accepted Answer

The given code represents John's salary per month after working a certain number of months (denoted by the code). Therefore, 11ec1b6e_3c5e_c92a_bbf8_0164c9c50701_TBX8728_11 would represent John's salary after working 3 months at the job.

Question 15

Find the vertex of  .

Accepted Answer

The answer of Find the vertex of  .
...

Question 16

Find the maximum or minimum value of the quadratic function  .

Accepted Answer

To find the maximum or minimum value of a quadratic function in the form of ax^2 + bx + c, we use the formula -b/2a to find the x-coordinate of the vertex (the highest or lowest point of the parabola). Plugging in the values given in the problem, we get x = -(5/2). To find the corresponding y-coordinate (the maximum or minimum value), we plug in this x value into the original equation: 
11ec1b6e_3c60_ec46_bbf8_3b909e74a5f2_TBX8728_11 = 4(-(5/2))^2 + 20(-(5/2)) + 7
Simplifying, we get 11ec1b6e_3c60_ec49_bbf8_bbad64df7b5c_TBX8728_11 as the minimum value. Thus, the answer is D.

Question 17

Find a quadratic function g whose graph is shown below.

Accepted Answer

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

Question 18

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 .

Accepted Answer

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

Question 19

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 .

Accepted Answer

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

Question 20

Express  in the standard form of a quadratic function.

Accepted Answer

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

Quiz 5: Quadratic Functions and Models

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.

Using the graph below, find the x -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 ?

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

Find the vertex of .

Express in the standard form of a quadratic function.

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

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

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

Express in the general form of a quadratic function.

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

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 ?

Find the vertex of .

Find the maximum or minimum value of the quadratic function .

Find a quadratic function g whose graph is shown below.

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 .

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 .

Express in the standard form of a quadratic function.