CPM Homework Help : APCALC Problem 4-165

Theresa loves tangents! This time, she has drawn several tangents and erased her original function. What is the equation of her original function?

Hint:

It looks like a transformation of $y = x^2$ .

7 segments with approximate slopes at centers as follows: @ (negative 3, comma 8) with slope of negative 4, @ (negative 2, comma 3), slope of negative 2, at (negative 1, comma 0), slope of negative 1, at (0, comma negative 1), slope of 0, at (1, comma 0), slope of 1, at (2, comma 3), slope of 2, at (3, comma 8), slope of 3.