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
?