Game Development Reference
In-Depth Information
To experiment, insert the following values in the field preceding the plus sign and
observe the results: 2, 3, 5, 6. In each instance, the distance you shift the graph to
the left on the
x
axis changes. To shift the graph so that its vertex moves to the
right, use values of
2,
3, and
6. As you go, remember to click on the Chart
for Formula 1 button to refresh the graph each time you change a value. Also,
increase the value of the X Range To control to 12.
Conclusion
This chapter has provided a context in which you have explored several types of
work related to linear equations. Exploring how to calculate slopes allowed you
to gain a stronger sense of the way that coordinate pairs relate to each other. You
extended this understanding to encompass use of the Pythagorean theorem,
which allowed you to calculate the distances separating points on a line. From
there, you moved on to investigate the slopes of lines and their inverses, which
enabled you to find perpendicular lines.
You also worked with such things as translation of lines and symmetry, and these
activities will prove important as you move on to work with quadratic and other
equations. When you explored absolute values, you were able to generate sym-
metrical lines by mirroring positive and negative values. In your explorations of
symmetry relative to points, axes, and lines, you saw that if you generate values
that are the square of
x
, you arrive at a line that is symmetrical to the
y
axis. If you
generate values that are the cube of
x
, you arrive at a line that is symmetrical to
the
origin
of the Cartesian plane. Still other lines are symmetrical to the line you
create with the equation
x ΒΌ y
.
