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

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

Example 2 Sketch the following curves y = -x3 x -3 -2 -1 1 2 3 y 27 8 1 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

Today’s work Cubic Worksheet