Finding the formula for a parabola and its antiderivative graph.

Question

For part a) i have : $f'(x)= 3x^2-18x+15$

Can someone provide a straightforward, simple explanation for part b)? Best if no hints are given just an answer with the explanation please.

Answer 1

$f(x)=x^3-9x^2+15x+15$. An antiderivative of $3x^2 -18x +15$ is $x^3-9x^2+15x+{}$constant, and the constant is the $y$-intercept of the function.

Answer 2

You don't want the the derivative of your parabola -- you want the antiderivative.

Just think to yourself "What could I take the derivative of to get $3x^2$? What about $-18x$? And what about $15$?"

Then once you've figured that out, you just need to add a constant $C$ to your answer, because the derivative of a constant would be zero. Then knowing that your graph goes through the point $(0,15)$, solve for $C$.