Quadratic Functions Worksheet - Chapter 2 Page 10
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1102Chapter02_014_024.qxd
3/9/04
9:31 am
Page 23
Quadratic functions
2
Find the values of k for which x
kx
4
0 has equal roots.
2
2
Find the values of k for which kx
8x
k
0 has equal roots.
3
Mixed exercise
2G
x
1
Draw the graphs with the following equations, choosing appropriate values for
.
For each graph write down the equation of the line of symmetry.
y
x
2
x
y
x
2
x
a
6
5
b
2
3
4
Solve the following equations:
2
y
2
y
x
2
x
a
3
2
0
b 3
13
10
0
x
2
x
x
x
2
c 5
10
4
3
d (2
5)
7
3
Solve the following equations by:
i
Completing the square.
ii Using the formula.
x
2
x
x
2
x
a
5
2
0
b
4
3
0
x
2
x
x
2
x
c 5
3
1
0
d 3
5
4
Sketch graphs of the following equations:
4
y
x
2
x
y
x
2
x
a
5
4
b
2
3
2
2
c
y
6
10
x
4
x
d
y
15
x
2
x
x
Given that for all values of
:
5
x
2
x
x
2
3
12
5
p(
q)
r
a Find the values of p, q and r.
2
E
x
x
b Solve the equation 3
12
5
0.
Find, as surds, the roots of the equation
6
Hint: Remember roots
mean solutions.
2
2(
x
1)(
x
4)
(
x
2)
0
E
Use algebra to solve (
x
1)(
x
2)
18.
7
23
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