# Determine the quadratic function whose graph is given

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

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

\$\displaystyle f(-1)=5\$

\$\displaystyle f(0)=-1\$

\$\displaystyle f(3)=5\$

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