Question

The question is in the photo. Determine an equation for the pictured graph. Please help!!

Answer 1

Answer: (x+1)^3*(x-2)

Explanation:

It's probably not obvious, but the squiggly portion through the x intercept x = -1 is a triple root. This is because this portion resembles a cubic graph. If instead it was a more straightish line through this root, then we'd have a single root.

So because x = -1 is a triple root, this means the factor (x+1) has the exponent 3. We have the factor (x+1)^3

The other factor is (x-2) from x = 2 being the other root.

All together we have (x+1)^3*(x-2) as the complete factorization. The leading coefficient is 1 to have this graph open upward. Or put another way, since the end behavior is going to positive infinity for both endpoints, the leading coefficient must be positive.