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May 24th









May 24th

Math 131 Chapter 3 Problem Set

1.

The graph of a quadratic function is
given. Select the function's equation from
the choices
given.

Choose the correct equation below.

 

2.

In the fol lowing exercise , find the coordinates of the vertex for the parabola defined by
the given quadratic function.

 
The vertex is .(Type an ordered pair .)

3.

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the
equation of the parabola's axis of symmetry. Use the graph to de termine the function 's
domain and range.

 
The vertex is ().
(Type an ordered pair. Simplify your answers .)

The axis of symmetry is x= .
(Type an integer or a reduced fraction . Type N if there is no axis of symmetry.)

The y-intercept is .
(Type an integer or a reduced fraction. Type N if there is no y-intercept.)

The x-intercept is .
(Type an integer or a reduced fraction. If there is more than one x -intercept, use
commas to separate the values. Type N if there are no x-intercepts..)

Choose the correct graph for f(x)



What is the domain of f(x)?

All real numbers
All negative numbers


What is the range of f(x)

4.

David has available 280 yards of fencing and wishes to enclose a rectangular area.
(a) Ex press the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
 

(a) Express the area as a function of the width.



(b) For what value of W is the area largest?

W = yards (Simplify your answer.)

(c) What is the maximum area?

A = square yards (Simplify your answer.)

5.

A rain gutter is made from sheets of
aluminum that are 14 inches wide
by turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-sectional
area and allow the greatest
amount of water to flow. What is
the maximum cross-sectional area?
 
The cross-sectional area is maximized when the depth of the gutter is inches.

The maximum cross-sectional area is square inches.

6.

Determine the graph's end behavior. Find the x-intercepts and y-intercept. Determine
whether the graph has symmetry. Determine the graph of the function.

 
a. Use the leading coefficient test to determine the graph's end behavior. Which
statement describes the behavior at the ends of f(x) ?

The graph rises to the left and falls to the right .
The graph falls to the left and rises to the right
The graph falls to the left and  to the right .
The graph rises to the left and to the right .

b. What are the x-intercepts?

x=  (Use a comma to separate answers as needed.)

At which x-intercept(s) does the graph cross the x-axis?

x=
(Use a comma to separate answers as needed. Type N if there is no solution.)

At which x-intercept(s) does the graph touch the x-axis and turn around?

x=
(Use a comma to separate answers as needed. Type N if there is no solution.)

c. Find the y-intercept by setting x equal to 0 and computing f(0).
The y-intercept is y= .

d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
Choose the correct answer below.

origin symmetry
y-axis symmetry
None of the above

e. Determine the graph of the function. Choose the correct graph below. Use the fact
that the maximum number of turning points of the graph is n -1, with n as the leading
term to check the correct choice.

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