# Math Help - Finding the equation of a parabola from given information.

1. ## Finding the equation of a parabola from given information.

Hi all, any help with this problem would be much appreciated.
I have to find a quadratic equation, and am given this information.
points (2,11) and (-1 and 2) lie on the graph.
x=2 when gradient =6.
I know this involves simultanous equations to find a, b and c, however i don't know what equations I have to use!
Thanks for any help anyone could provide!!!!!

2. Originally Posted by dominicc
Hi all, any help with this problem would be much appreciated.
I have to find a quadratic equation, and am given this information.
points (2,11) and (-1 and 2) lie on the graph.
x=2 when gradient =6.
I know this involves simultanous equations to find a, b and c, however i don't know what equations I have to use!
Thanks for any help anyone could provide!!!!!
f(x) = a^2 + bx + c.

f(2) = 11 and f(-1) = 2. Furtherfore f'(2) = 6. Write down the equations corresponding to these three conditions and solve them for a, b and c.

3. By 'f'(2) = 6', does this mean 4a+b=6, or am I wrong with this?

4. If $f(x)= ax^2+ bx+ c$, then $f '(x)= 2ax+ b$ so $f '(2)= 2a(2)+ b= 4a+ b= b$. Yes, you are correct. You have three equations to solve for a, b, and c.