Quadratic Function from 2 points

[cpags68]

Given f(x)=ax^2+bx+c, with a not equal to 0; the equation f(x)=5 has exactly one solution, x=2; and f(5)=8.
Find the vertex of the graph y=f(x).

 

[skeeter]

the vertex form of a quadratic function is

[MATH]f(x) = a(x-h)^2 + k[/MATH]
where [MATH](h,k)[/MATH] is the vertex.

Using that form, what would be the function value of [MATH]f(h)[/MATH]?

Would any other value of x yield that same value?