Question

Determine the quadratic function f whose vertex is (3,-2) and passes through(1,6)

f(x) = ax^2 + bx + c

Answer 1

from the vertex, we know

f(x) = a(x-3)^2 - 2
Since f(1) = 6,
6 = a(1-3)^2 - 2
a = 2

f(x) = 2(x-3)^2 - 2
= 2x^2 - 12x + 16