# Determine the quadratic function whose graph is given

• January 8th 2013, 10:11 PM
alex95
Determine the quadratic function whose graph is given
Hi All,

I would really appreciate some help/hints for the following problem I am stuck on.
Determine the quadratic function whose graph is given:
The function has given points at (-1,5), (3,5), and y-intercept at (0,-1)

I know that the axis of symmetry (h) is at 1 because it is the mid-point between -1 and 3. If I plug that into the function a(x-h)^2 + k, I still have two unknowns, a and k
a(x-1)^2+k
Can someone please explain to me how to solve this. Thank you very much in advance.

Alex
• January 8th 2013, 10:21 PM
MarkFL
Re: Determine the quadratic function whose graph is given
Let:

$f(x)=ax^2+bx+c$ and use the given points to state:

$f(-1)=5$

$f(0)=-1$

$f(3)=5$

The second equation tells you $c=-1$, and this along with the first and third equations will give you two equations and two unknowns.