Quadratic Functions Worksheet - Chapter 2 Page 9
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1102Chapter02_014_024.qxd
3/9/04
9:31 am
Page 22
2
CHAPTER
Example
14
y
x
2
x
Sketch the graph of
5
4
a
0 so it is a
shape.
When y
0,
2
x
0
5x
4
Factorise to solve the equation.
0
(x
4)(x
1)
(You may need to use the formula or
complete the square.)
x
4 or x
1
So x-axis crossing points are
(4, 0) and (1, 0).
When x
0, y
4, so y-axis crossing
point
(0, 4)
a
1, b
5, c
4
2
b
25, 4ac
16
2
So b
4ac and a
0.
Remember general shape:
So sketch of the graph is:
y
(0, 4)
(1, 0)
(4, 0)
0
x
Label the crossing points.
Example
15
2
Find the values of k for which x
kx
9
0 has equal roots.
2
x
kx
9
0
Here a
1, b
k and c
9
2
For equal roots use b
4ac
2
k
4
1
9
So
k
6
Exercise
2F
Sketch the graphs of the following equations:
1
y
x
2
x
y
x
2
x
y
x
2
x
y
x
2
x
a
3
2
b
3
10
c
2
15
d
2
7
3
y
x
2
x
y
x
2
x
y
x
2
x
y
x
2
x
e
2
3
f
6
19
10
g
3
2
5
h
3
13
y
x
2
x
y
x
x
2
i
6
7
j
4
7
2
22
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