How do you find the cubic equation from its graph?

Question

Does anyone know how you would fit three cubic polynomials on a parabola with 2 turning points? Like use points on the graph and a formula to find the equations? The parabola given does not intercept the x-axis (as it has domain restrictions).

 

Also, how would you repeat this, but with three polynomials of order 4?

 

Answer 1

If you know the function algebraically, and it's a polynomial of degree n, then you don't do any "fitting." It is what it is!

 

If you have a bunch of points to plot and it looks as if a smooth curve passing through those points would be a parabola, then you ask your calculator to fit that type of curve to it (by requesting a quadratic fit). If the apparent graph would be cubic (e.g. one end up, other end down, among other common characteristics such as two turning points), then you request a cubic fit.

Etc, etc.