Game Development Reference
In-Depth Information
Figure 9.4
A negative coefficient establishes a downward slope.
this situation if you apply a negative coefficient to the
x
variable of the quadratic.
Figure 9.4 illustrates the effect of a negative coefficient. On the top, the parabola
opens upward. The coefficient of
x
establishes a positive slope, so the parabola
opens upward. On the bottom, the coefficient is negative, and the result is that the
values you generate establish a negative slope. The parabola opens downward.
Widening a Parabola
As you can change a quadratic equation so that its vertex opens up or down, so
you can change the width of a parabola. As with direction of the vertex, you
adjust the coefficient of the
x
in a quadratic to change the width. If you make the
value of the equation less than 1, then the parabola becomes less steep. Its mouth
widens. Its rate of climb becomes less pronounced. Figure 9.5 illustrates this
