Question

What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9,9)?


f(x) =
(x −
)2 +

Answer 1

Vertex form: f(x) = a(x − h)^2 + k with (h,k) = (7,−3). Use (9,9):

9 = a(9−7)^2 − 3 → 9 = 4a − 3 → 4a = 12 → a = 3.

So f(x) = 3(x − 7)^2 − 3.