# Thread: 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: $\displaystyle 1 = d$ .... (1)

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

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

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

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

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