Name______________________________________

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Name______________________________________ Date_______________ Period_________

SOLVE BY GRAPHING WORKSHEET

Graph each function. State the domain, the vertex , the range, the x-intercepts, and the axis of symmetry.

y

1.)

f(x)= x

2

+ 4

Domain: ________

Range: ________

Vertex:________

Max or min?________

5

4

3

2

1

7

6

10

9

8

1 2 3 4 5 6 7 8 9 10 x

x

-intercepts: ____________

Axis of symmetry: ________

-2

-3

-7

-8

-9

-10

-4

-5

-6

2.)

h

(

x) =

-

x

2

– 2

x

+ 8

Domain: ________

Range: ________

Vertex:________

Max or min?________

x

-intercepts: ____________

Axis of symmetry: ________

-8

-9

-10

-2

-3

-4

-5

-6

-7

7

6

5

4

3

2

1

10

9

8 y

1 2 3 4 5 6 7 8 9 10 x

Without graphing the quadratic functions, complete the requested information:

3.)

2

x

2

9

x

3

4.)

 

2

3

x

2

2

x

5

What is the direction of opening? _______

What is the direction of opening? _______

Is the vertex a max or min? _______

Wider or narrower than

y

=

x

2

? ___________

Is the vertex a max or min? _______

Wider or narrower than

y

=

x

2

? ___________

5)

Graph: y = x

2

– 7x + 10. Answer the following questions.

What is the axis of symmetry? __________

What are the coordinates of the vertex?________

Is the vertex a max or minimum point? ________

How many roots are there?__________

What are the solutions of this equation? _____

What are the solutions called? ________

6)

Graph: y   x -6x - 5

.

Answer the following questions.

What is the axis of symmetry? __________

What are the coordinates of the vertex?_______

Is the vertex a max or minimum point? ________

How many roots are there?__________

What are the solutions of this equation? ________

What do you call these solutions? __________

For #7-8, a quadratic function and its graph are shown. Identify the solutions, or roots, of the related quadratic equation.

7.)

g

(

x) = 3x

2

3x – 6

8.) h (

x) = -2x

2

+ 6x

Solve

:

x = ____ or ____

Solve

:

x = ____ or ____

For #9-10, a quadratic function and its graph are shown. Identify the solutions, or roots, of the related quadratic equation.

9.)

f

(

x) = x

2

– x – 2

10.) y = -x

2

+ 9

Solve

:

x = ____ or ____

Solve

:

x = ____ or ____

Find the vertex of each parabola. Graph the function and find the requested information

11.)

f(x)= x

2

– 2

x

– 3

a

= ____,

b

= ____,

c

= ____ y

10

Vertex: _______

7

6

5

4

3

2

1

9

8

Max or min? _______

Direction of opening? _______

Wider or narrower than

y

=

x

2

?

9 10 x

-2

-3

-4

-5

-6

-7

-8

-9

-10

1 2 3 4 5 6 7 8

x

_______________

Domain: ________

Range: ________

-intercepts: ____________

Axis of symmetry: ________

12.)

g

(

x) = -2x

2

+

8x – 5 a

= ____,

b

= ____,

c

= ___ y

10

9

8

7

6

5

4

3

2

1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

1 2 3 4 5 6 7 8 9 10 x

Vertex: _______

Max or min? _______

Direction of opening? _______

_______________

Domain: ________

Range: ________

x

-intercepts: ____________

Axis of symmetry: ________

Wider or narrower than

y

=

x

2

?

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