Game Development Reference
In-Depth Information
Substituting these values into the quadratic formula, you arrive at this equation:
p
3
2
x ¼
3
4
ð
2
Þð
7
Þ
2
ð
2
Þ
p
9
þ
56
x ¼
3
4
p
65
x ¼
3
4
For a solution set, you can use a calculator to arrive at a decimal value that
represents the root or an approximation of the root:
x
3
8
:
06
11
06
4
2
:
:
756
4
x
3
þ
8
:
06
5
:
06
4
1
:
265
4
The Discriminant
In the quadratic equation, you refer to the expression
4
a
p
as the dis-
criminant. The result of the expression allows you to determine the values that
are acceptable as solutions of the quadratic formula:
b
2
If you find that
b
2
4
ac ¼
0, then the equation possesses only one real
n
number solution.
If you find that
b
2
4
ac
>
0, then two real number solutions satisfy the
n
equation.
If you find that
b
2
4
ac
<
0, then no real number solution exists for the
n
equation.
As mentioned previously, the values you arrive at when you examine the dis-
criminant allow you to determine whether the lines of the parabola the equation
generates intersect with the
x
axis.