Question

Construct a polynomial function that might have the graph. Yes, you guessed

it, there could be more than one answer! Only give me one of the possibilities.
Leave your answer in factored form.

Answer 1

There is a 'strike-through' root at -1 and a double root at 2, so the equation is of the form

`y=a(x+1)^3 (x-2)^2`

Since the y-intercept is 4,

`4=a(0+1)^3(0-2)^2 \implies 4a=4 \implies a=1 \\ \\ \therefore \boxed{y=(x+1)^3 (x-2)^2}`