Quadratic Functions Worksheet - Chapter 2 Page 8
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1102Chapter02_014_024.qxd
3/9/04
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Page 21
Quadratic functions
Exercise
2E
Solve the following quadratic equations by using the formula, giving the solutions in surd form.
Simplify your answers.
x
2
x
x
2
x
3
1
0
3
2
0
1
2
x
2
x
x
2
x
3
6
6
0
4
5
2
0
2
2
3
x
10
x
2
0
4
x
4
x
1
0
5
6
x
2
x
x
2
x
7
9
1
0
5
4
3
0
7
8
x
2
x
x
2
x
4
7
2
10
11
2
7
0
9
2.6
You need to be able to sketch graphs of quadratic equations and solve problems
using the discriminant.
The steps to help you sketch the graphs are:
1
Decide on the shape.
When a is
0 the curve will be a
shape.
When a is
0 the curve will be a
shape.
x-
y
2
Work out the points where the curve crosses the
and
-axes.
y
x
Put
0 to find the
-axis crossing points coordinates.
x
y
Put
0 to find the
-axis crossing points coordinates.
2
3
Check the general shape of curve by considering the discriminant, b
4ac.
When specific conditions apply, the general shape of the curve takes these forms:
2
2
2
b
4ac and a
0
b
4ac and a
0
b
4ac and a
0
y
y
y
0
0
0
x
x
x
You can use the
discriminant to establish
Here there are two
Here there are two
Here there are no
when a quadratic
different roots.
equal roots.
real roots.
equation has
●
2
equal roots: b
4ac
2
2
2
b
4ac and a
0
b
4ac and a
0
b
4ac and a
0
●
2
real roots: b
4ac
y
y
y
●
no real roots: b
2
4ac
0
0
0
x
x
x
Here there are two
Here there are two
Here there are no
different roots.
equal roots.
real roots.
21
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