Question

The graph in the xy plane of the quadratic function f contains the points (0,0),(1,5),(5,5) What is the maximum value of f(x)?

Answer 1

notice that (1,5) and (5,5) have the same y value, so the vertex must be half way at x = 3
so the equation looks like
y = a(x - 3)^2 + c
also (0,0) lies on it, so
0 = 9a + c
and (1,5) lies on it, so
5 = 4a + c
subtract:
-5 = 5a
a = -1
in 0=9a + c
0 = -9+c ----> c = 9

our function is y = -(x-3)^2 + 9
which has a maximum value of 9