Method To plot a graph of a cubic function: 1. Isolate y on one side of the equation. 2. Substitute the values of x in the domain to fi nd the corresponding values of y. 3.
Plot y = x 3 + 4x 2 + x − 6 in the domain −4 ≤ x ≤ 2, x ∈ R.
Solution
x −4 −3 −2 −1 0 1 2 y −10 0 0 −4 −6 0 20
y
12 16 20
4 8
–4 –3 –2
–1 0 –4
–8 1 2 3 4 x
Plot the y values on the vertical axis against the x values on the horizontal axis. EXAMPLE 2
ACTIVITY ACTION CTION
Plotting cubic functions
OBJECTIVE To draw a number of cubic functions
Y 7
General shape of cubic functions
The sign of a in the cubic function y = f (x) = ax 3 + bx 2 + cx + d tells you the general shape of the cubic graph. y = 4x 3 − 9x 2 + 11x − 2 a = 4 > 0
