Quadratic Functions Worksheet - Chapter 2 Page 5
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1102Chapter02_014_024.qxd
3/9/04
9:31 am
Page 18
2
CHAPTER
Example
9
Complete the square for the expressions
x
2
x
x
2
x
a
12
b 2
10
a x
2
12x
2b
12, so b
6
2
2
(x
6)
6
2
(x
6)
36
2
x
2
b
2x
10x
Here the coefficient of
is 2.
x
2
2
So take out the coefficient of
.
2(x
5x)
5
5
x
2
x
Complete the square on (
5
).
2
2
2[(x
)
(
)
]
2
2
5
2
5
Use b
5.
2
2(x
)
2
2
Exercise
2C
Complete the square for the expressions:
x
2
x
x
2
x
x
2
x
x
2
x
1
4
2
6
3
16
4
5
x
2
x
6
x
2
x
7
x
2
x
8
x
2
x
14
2
16
3
24
2
4
9
x
2
x
10
x
2
x
11
x
2
x
12
x
2
x
5
20
2
5
3
9
3
2.4
You can solve quadratic equations by completing the square.
Example
10
x
2
x
Solve the equation
8
10
0 by completing the square.
x
2
8x
10
0
x
2
Check coefficient of
1.
x
2
8x
10
x
2
Subtract 10 to get LHS in the form a
b.
2
2
x
2
x
(x
4)
4
10
Complete the square for (
8
).
2
2
(x
4)
10
16
Add 4
to both sides.
2
(x
4)
6
(x
4)
6
Square root both sides.
x
4
6
Subtract 4 from both sides.
Then the solutions (roots) of
Leave your answer in surd form as this is a
non-calculator question.
2
x
8x
10
0 are either
x
6 or x
4
4
6 .
18
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