Question

What function has a vertex at (5,4) and contains the point (-1,40)?

Answer 1

f(x) = (x - 5)^2 + 4.

Explanation:

The vertex form of a parabola is

f(x) = a(x - h)^2 + k where the vertex is at (h, k) and a is some constant.

So here we have:

f(x) = a(x - 5)^2 + 4

Now when x = -1 , f(x) is 40 so:

40 = a(-1-5)^2 + 4

36a = 40 - 4 = 36

a = 1.

So the function is f(x) = (x - 5)^2 + 4