2. Cubic functions
As we have seen a function in which the highest power of x is 3 is called a cubic function.
The general form of a cubic function is:
y = ax3 + bx2 + cx + d
DON’T PANIC
In this course the cubics we will look at will be of the form:
y = ax3
Some examples are y = x3, y = 5x3, y = ½x3, y = 2x3, and

3. Example 1 Sketch the following curves y = x3 x -3 -2 -1 1 2 3 y -27 -81 2 3 y
-27 -8 -1 1 8 27
y = 2x3 x -3 -2 -1 1 2 3 y
-54
-16 -2 2 16 54
y = ½x3 x -3 -2 -1 1 2 3 y -4 -½ 4
-13·5
13½

4. Example 2 Sketch the following curves y = -x3 x -3 -2 -1 1 2 3 y 27 81 2 3 y 27 8 1 -1 -8
-27
y = x3 + 8 x -3 -2 -1 1 2 3 y
-19 7 8 9 16 35
y = (x + 1)3 x -3 -2 -1 1 2 3 y -8 -1 1 8 27 64

5. Today’s work
Cubic Worksheet