Quadratic Functions Worksheet - Chapter 2 Page 2
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1102Chapter02_014_024.qxd
3/9/04
9:31 am
Page 15
Quadratic functions
Exercise
2A
Draw graphs with the following equations, taking values of
x
from
4 to
4.
For each graph write down the equation of the line of symmetry.
y
x
2
y
x
2
3
5
1
2
1
2
2
y
x
y
x
3
4
2
Hint: The general shape
for part 4 is an upside
2
2
y
x
y
x
x
5
(
1)
6
3
2
down
-shape. i.e.
.
y
x
2
x
y
x
2
x
7
2
3
5
8
2
6
y
x
2
9
(2
1)
2.2
You can solve quadratic equations using factorisation.
Quadratic equations have two solutions or roots. (In some cases the two roots are equal.)
x
2
x
To solve a quadratic equation, put it in the form a
b
c
0.
Example
2
x
2
x
Solve the equation
9
2
x
9x
x
2
x
Rearrange in the form a
b
c
0.
2
x
9x
0
x(x
9)
0
x
Factorise by
(factorising is in Chapter 1).
Then either part of the product could be zero.
Then either x
0
0 ⇒ x
x
or
9
9
So x
0 or x
A quadratic equation has two solutions
9 are the two solutions
(roots). In some cases the two roots are
2
of the equation x
9x.
equal.
Example
3
2
Solve the equation
x
2
x
15
0
x
2
2x
15
0
(x
3)(x
5)
0
Factorise.
0 ⇒ x
Then either x
3
3
0 ⇒ x
x
or
5
5
The solutions are x
3 or x
5.
15
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