Answer:
f(x) = 2(x - 6)² - 3
Explanation:
f(x) = a(x - h)² + k ← vertex form of parabola equation with vertex (h, k)
So:
f(x) = a(x - 6)² + (-3)
f(x) = a(x - 6)² - 3 ← vertex form of our parabola equation
Parabola goes through (8, 5) so if x=8 then f(x)=5
5 = a(8-6)² - 3
5 +3 = a(2)² - 3 +3
8 = 4a
a = 2
That means, the equation of a parabola with vertex (6, -3) and passing through the point (8, 5):
f(x) = 2(x - 6)² - 3