Game Development Reference
In-Depth Information
4. Select Value from the menu, and then click to place the Value field after
the plus sign. This is the y-intercept of the equation. To raise the vertex
of the parabola 3 units above the x axis, type 3.
5. Now proceed to the lower-right panel and click the Chart for Formula 1
button to generate the graph. As Figure 10.25 illustrates, the vertex of the
parabola that results rests above the
x
axis.
The y-intercept forced the top parabola in Figure 10.25 to shift three units above
the
x
axis. To generate the bottom parabola, perform the following steps:
1. Click the menu item for Value. Then click in the lower equation compo-
sition area to position the Value field. Type x in the Value field.
2. Click the Power menu item. Position the field for the exponent to the upper
right of the Value field. Type 2 in the Power field.
3. Click the Subtract menu item. To position the minus sign, click to the right
of the Value field.
4. Click Value in the menu. To position the Value field, click after the minus
sign. To lower the vertex of the parabola 3 units below the x axis, type 3.
5. In the Chart panel, set the x axis and y axis Zoom fields to 1 and
3,
respectively.
6. In the lower-right panel, click the Chart for Formula 2 button to generate
the graph. As Figure 10.25 illustrates, the vertex of the graph that appears
rests three units below the
x
axis.
Parallel Lines
The general form of the line's slope-intercept equation is
y ¼ mx þ b
. In this
equation,
m
describes the slope of the equation, and
b
provides the value of the
y-intercept. Given that a set of equations possesses the same slope, if you vary
only the value of
b
, you end up with a set of parallel lines.
Figure 10.26 illustrates the graphs of three lines. The middle line crosses the
origin of the Cartesian plane. You could rewrite it as
y ¼ x þ
0. The other two
lines include positive and negative values for the y-intercept. The top line pro-
vides a y-intercept of 3. The lower line provides a y-intercept value of
3.
