Answer:
f(x) = 4(x - 4)² - 4
Step-by-step explanation:
f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)
so the equation of parabola with the vertex (4, -4) is
f(x) = a(x - 4)² - 4
passes through the point (2, 12) means if x=2 then f(x)=12
12 = a(2 - 4)² - 4
12 +4 = a(-2)² - 4 +4
16 = 4a
a = 4
Therefore the equation (in vertex form) of parabla is:
f(x) = 4(x - 4)² - 4
