Parabola given two equations

Hi friends,

My stepdaughter came to me today explaining a sum she got in the exam. I believe I have understood her right, so here is the problem....I did some of it..

$f(x)=a(x+2)^2+c$

$g(x)=(2x+5)(x+b)$

Nothing else is given. Calculate a, b and c. Apparently both equations point to the one and same parabola.

So I said:

The axis of simmetry lies on $x=-2$

The x intercepts are $x=-{5 \over 2}$ and $x=-b$

Now since the one x intercept lies on -2.5, and the axis of simmetry is on the x=-2, it tells me the other x intercept has to be -1.5

So, $b=1.5$

From here I'm stuck. Please help me with this...as usual, all help is greatly appreciated!