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DATE:
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ALGEBRA: LESSON 9.2 SOLVING QUADRATIC EQUATIONS BY GRAPHING
FOCUS LEARNING TARGET #1
c I can determine the number of solutions to a quadratic equation by looking at a graph.
How do you locate the SOLUTIONS (ROOTS) on a graph of a quadratic equation?
me roots
X-intercepts
the
are
·
·
of
the
graph
.
Example 1: Identify the solutions (roots)
of the graph to the left. Write the solutions
(roots) as ordered pairs).
(-4 , 0)
and
(0 , 0)
Example 2: Graph x2 – x = 6. Find the solutions (roots).
Step 1: Write the equation in the standard form ax2 + bx + c = 0.
-x
X
-
6 = 0
e
·
6
c = ___________
-
-
Step 3: Find the x-coordinate of the vertex and the equation of the axis of symmetry.
−b
=
x=
2a
=
x
Step 4: Make a symmetrical table of values.
Step 5: Find the x-intercepts from the table.
y
€
-
2
y
-
1
y= (
y0y
=
=
-
(2)-(2)
12 ( 1)
-
-
(0)2 (d)
-
-
-
Vertex
3=(2) (2)
-
I
b = __________
I
a = __________
Step 2: Identify a, b, c.
1
2
y=
y
33
-
= -
=
6
4
0
-
-
=
0
(-2 0) and (3 0
_______________________________________
= -
4
Step 6: Graph.
6
6
b
=-
6
=
-
b
,
↑
6
,
Step 7: Check the solutions
algebraically.
In order to
-
2
check
and 3 into
x2 -X- 6
(2)" ( 2)
-
4+2
(3)2 (3)
9
-
9
-
-
6
=
0
6 =0
0 = 0
/
6
0
-
=
0 =0
substitute
=
0
/
=
0
ALGEBRA: LESSON 9.2 SOLVING QUADRATIC EQUATIONS BY GRAPHING
Example 3: Graph and find the solutions (roots).
Y3
a = __________
Find a, b, c.
# −1&
y = % (x 2 + 3
$ 3'
3
c = __________
O
b = __________
-
€
Find the x-coordinate of the vertex and the equation of the axis of symmetry.
Vertex
:b
==
Make a table of values.
x
-
-3
9
&
O
Vertex
0
3
3
O
6
Graph.
y
-6
0
-
D
&
9
D
⑧
-
*
Find the solutions (roots) of the quadratic equation.
(-3 , 0)
and (3 %)
,
Check the solutions algebraically.
substitute
and
X = -3
-
X= 3
(3) 3)2 + 3
-
-
Y3
into
y
=x
+ 3
ALGEBRA: LESSON 9.2 SOLVING QUADRATIC EQUATIONS BY GRAPHING
Example 4: Graph and find the solutions (roots).
I
a = __________
Find a, b, c.
x2 + x = 12
x+ X 12
-
↓
b = __________
= 0
12
c = __________
-
Find the x-coordinate of the vertex and the equation of the axis of symmetry.
x2+ X 12
Make a table of values.
x
y
-=
a
-
⑧
-Y
-
Graph.
3
-
6
Y
o
-2
-1
-
Y
8
-
-
-
-
12
R
12
I
-
2
-
I
10
10
b
&
&
a
⑧
⑧
O
Find the solutions (roots) of the quadratic equation.
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