# Math Help - Finding the equation of a cubic from given information

1. ## Finding the equation of a cubic from given information

one last question:

The graph of the function y = ax^3 + bx^2 + cx + d has a maximum turning point at (0,1) and a minimum turning point at (-2, -2). Find the values of the coefficients.

I managed to get c = 0 and 3a - b = 0, but thats it..help?

2. Originally Posted by duskmantle
one last question:

The graph of the function y = ax^3 + bx^2 + cx + d has a maximum turning point at (0,1) and a minimum turning point at (-2, -2). Find the values of the coefficients.

I managed to get c = 0 and 3a - b = 0, but thats it..help?
(0, 1) on curve: $1 = d$ .... (1)

(-2, -2) on curve: $-2 = -8a + 4b - 2c + d$ .... (2)

$\frac{dy}{dx} = 3a x^2 + 2bx + c$.

$\frac{dy}{dx} = 0$ when $x = 0$: $0 = c$ .... (3)

$\frac{dy}{dx} = 0$ when $x = -2$: $0 = 12a - 4b + c$ .... (4)

Solve the above equations simultaneously for a, b, c and d.