Instructor: Virginia Davis Course:

4/3/2016 Chapter 11 Review for Test Homework-Virginia Davis

https://xlitemprod.pearsoncmg.com/api/v1/print/math 1/11

1.

2.

3.

4.

5.

6.

Student: _____________________Date: _____________________

Instructor: Virginia DavisCourse: Foundations for College Math(1)

Assignment: Chapter 11 Review forTest Homework

Use the square root property to solve the equation. The equation has real number solutions.

4z − 562

= 0

z =

(Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as

needed.)

Use the square root property to solve the equation. The equation has real number solutions.

(3x + 7)2= 27

x =

(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Solve the equation by completing the square. The equation has real number solutions.

x + 5x − 12

= 0

x =

(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

An isosceles right triangle has legs of equal length. If the

hypotenuse is centimeters long, find the length of each leg.28

x

x

28

Each leg is cm long.

(Simplify your answer. Type an exact answer, using radicals as needed.)

Use the quadratic formula to solve the equation. The equation has real number solutions.

y− 3 = 2y2+ 1

y =

(Type a simplified answer, using fractions and radicals as needed. Use a comma to separate answers as needed.)

Use the quadratic formula to solve the equation.

2x − x + 9 = 02

x =

(Type an exact answer, using radicals and as needed. Use a comma to separate answers as needed.)



7.

8.

9.

10.

11.

12.

(1) two real solutions. two complex but not real solutions. one real solution.

Use the discriminant to determine the number and types of solutions of the quadratic equation.

− 6x = − 3x + 12

The equation has (1)

A ball is thrown downward from the top of a foot building with an initial

velocity of feet per second. The height of the ball h after t seconds is given

by the equation

140

10

h = − 16t − 10t + 140.2

How long after the ball is thrown will it strike the ground? 140 ft

sec

(Round to the nearest tenth as needed.)

Solve.

13

x+

3

x − 2=

x =

(Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals as

needed.)

Solve the quadratic inequality.

(x + 5)(x + 1) > 0

The solution set is .

(Type your answer in interval notation.)

Solve the inequality.

(x )(x )(x ) 0− 8 − 6 − 1 >

The solution set is .


Solve the inequality. Write the solution set in interval notation.

< 0x + 3

x − 6

The solution in interval notation is .




13.

14.

15.

Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.

h(x) = x + 52

Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.

The vertex is . (Type an ordered pair.)

The axis of symmetry is . (Type an equation.)

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y


f(x) = (x − 5)2




20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y


f(x) = (x − 2) + 72




20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y



16.

17.


h(x) = (x + 1) + 12


What is the vertex of the graph?


What is the equation for the axis of symmetry?

(Type an equation.)

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y


g(x) = 2x2


What is the vertex of the graph?The vertex is . (Type an ordered pair.)

What is the equation of the axis of symmetry? (Type an equation.)

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y



18. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.

f(x) = x + 8x + 72

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

Does the graph open upward or downward?

The parabola opens ward.upThe parabola opens ward.down

Find any xintercepts of the graph.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The xintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

B. There is no xintercept.

Find any yintercepts of the graph.


A. The yintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

B. There is no yintercept.

Use the graphing tool to graph the function.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y



19.

20.

21.

Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.

f(x) = − x + 2x + 82

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

Does the graph open upward or downward?

The parabola opens ward.downThe parabola opens ward.up

Find any xintercepts of the graph.


A. The xintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

B. There is no xintercept.

Find any yintercepts of the graph.


A. The yintercept(s) is(are) . (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

B. There is no yintercept.

Use the graphing tool to graph the function.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

If a baseball is projected upward from ground level with an initial velocity of feet per second, then its height is a function of time, given by s 16t t.

160= − 2 + 160

What is the maximum height reached by the ball?

The maximum height reached by the ball is feet.

Find the vertex of the graph of the following quadratic function.

f(x) = − x − 6x + 52




22.

23.

24.

Find the vertex of the graph of the following quadratic function.

f (x) = 5x + 10x − 22

The vertex is .

(Type an ordered pair.)

Find two numbers whose difference is and whose product is as small as possible.70

[Hint: Let x and x be the two numbers. Their product can be described by the function .]− 70 f(x) = x(x − 70)

The numbers are . (Use a comma to separate answers.)

The length and width of a rectangle must have a sum of . Find the dimensions of the rectangle that will have

the maximum area. [Hint: Let x and x be the length and width. The area can be described by the function

f(x) x( x).]

50

50 −

= 50 −

The length is and the width is .



1. , −14 14

2. ,− 7 + 3 3

3− 7 − 3 3

3

3. ,− 5 + 29

2− 5 − 29

2

4. 14 2

5. − , − 112

6. ,1 − 71

41 + 71

4

7. (1) two real solutions.

8. 2.7

9. 4 − ,4 +10 10

10. ( − , − 5) ( − 1, )

11. (1,6) (8, )

12. ( − 3,6)

13.

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y

(0,5)



x = 0

14.

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y

(5,0)

x = 5

15.

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y

(2,7)

x = 2

16.

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y



( − 1,1)

x = − 1

17.

20 16 12 8 4 4 8 12 16 20

20

16

12

8

4

4

8

12

16

20

x

y

(0,0)

x = 0

18. ( − 4, − 9)

The parabola opens ward.up

A. The xintercept(s) is(are) .( − 7,0),( − 1,0) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

A. The yintercept(s) is(are) .(0,7) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

19. (1,9)

The parabola opens ward.down

A. The xintercept(s) is(are) .( − 2,0),(4,0) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

A. The yintercept(s) is(are) .(0,8)



(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

20. 400

21. ( − 3,14)

22. ( − 1, − 7)

23. 35, − 35

24. 25

25

Instructor: Virginia Davis Course:

Documents

Transcript of Instructor: Virginia Davis Course: