Game Development Reference
In-Depth Information
Figure 9.11
A negative slope and a negative shift value invert the parabola and move it to the left, but you still shift
it upward 3 units.
The x-intercepts
The points at which the graph of the quadratic equation cross the
x
axis are
known as the
x
-intercepts. If you can determine the vertex of the parabola, and
know whether the parabola opens upward or downward, then you are in an
excellent position to calculate the
x
-intercepts. As the previous examples
reveal, not all quadratic equations have
x
-intercepts. For example, if a parabola
opens upward and is shifted upward from the
x
axis, it does not intercept the
x
axis.
Figure 9.12 provides a summary view of a few possibilities with respect to
quadratic equations. Accordingly, parabola A has one
x
-intercept because its
vertex lies on the
x
axis. The same is true of parabola C. Parabolas B and D have
