For points (3,4) and (-1,-3) what is the cubic equation

Question

 The graph has a turning point of (-1,-3) and another turning point of (3,4) what would the equation be of this cubic graph

Answer 1

Presumably what you mean by a turning point is either a maximum or a minimum.

For a general cubic you have 4 parameters (A, B, C, D) where the equation is f(x) = Ax³ + Bx² + Cx + D

The two points give you 2 linear equations in the 4 parameters.

The derivative = 0 at the points given so that you will have 2 more linear equations in the 4 parameters.

Thus, you will have a system of 4 linear equations in the 4 unknown parameters.

Solve that linear system for the 4 parameters.