Answer:
y = -2x^2(x - 3)
Step-by-step explanation:
Preliminary Remark
If a cubic is tangent to the x axis at 0,0
Then the equation must be related to y = a*x^2(x - h)
(3,0)
If the cubic goes through the point (3,0), then the equation will become
0 = a*3^2(3 - h)
0 = 9a (3 - h)
0 = 27a - 9ah
from which h = 3
From the second point, we get
4 = ax^2(x - 3)
4 = a(1)^2(1 - 3)
4 = a(-2)
a = 4 / - 2
a = -2
Answer
y = -2x^2(x - 3)
