Game Development Reference
In-Depth Information
To generalize then, solving for the two terms,
p
, it is necessary to
consider a set of observations that apply to the solutions of all quadratic equa-
tions. These observations are as follows:
p
and
If the value of
a
is greater than zero, then there are two solutions (
p
).
n
If the value of
a
equals zero, then only one solution is correct.
n
If the value of
a
is less than zero, no solution exists. (You cannot in this
situation find the square root of a negative number.)
n
Quadratic Appearances
You can draw on the discussion that previous chapters provided to explore a few
basic ideas that apply to representing quadratic equations. Consider, for exam-
ple, that quadratic equations possess a degree of 2. A variable with an exponent of
2 represents a square. When you graph values you generate using a square, the
values you generate are positive. For this reason, in the functional form of a
quadratic equation, the values of a domain (
x
) generate positive values of a
range (
y
). The resulting geometrical representation for this graph is a parabola.
Figure 9.1 illustrates a parabola generated by the equation
y ΒΌ x
2
.
Figure 9.1
A rudimentary quadratic function generates a parabola.