1. ## differentiate

Hi
I have been trying to solve this problem for a while but I don't understand how to do it. I know its related to finding deravatives and solving it.

Find values for a,b, and c such that the graph of y=ax^2 + bx + c has a relative maximum at (3,12) and crosses the y-axis at (0,1).

If anyone could explain me how to solve it it'll be greatly appreciated.

Thank you.

2. Let $f(x)=ax^2+bx+c$

$f'(3)=0\Rightarrow 6a+b=0$

$f(3)=12\Rightarrow 9c+3b+c=12$

$f(0)=1\Rightarrow c=1$

Now solve the system.