Name______________________________________ Date_______________ Period_________
SOLVE BY GRAPHING WORKSHEET
Graph each function. State the domain, the vertex , the range, the xintercepts, 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 #78, 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 #910, 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
?