Writing quadratic functions

Question

How would I write the quadratic function whose maximum value is 5 when x=2 and whose parabola passes through (1,12)?

Answer 1

f(x) = a(x - h)² + k

h = 2

k = 5

f(x) = a(x - 2)² + 5

12 = a(1 - 2)² + 5

12 = a + 5

a = 7

This contradicts the wording of the question. The point provided in the question must be a vertex, not a maximum. In this problem, since a > 0, the vertex is actually a minimum.

f(x) = 7(x - 2)² + 5