Answer:
f(x) = 3(x - 7)² - 4
Step-by-step explanation:
The vertex form of an equation of the parabola:
f(x) = a(x - h)² + k
the vertex is (7, -4) ⇒ h = 7, k = -4
so:
f(x) = a(x - 7)² + (-4)
f(x) = a(x - 7)² - 4
The parabola goes through the point (5, 8) ⇒ x=5, f(x)=8
8 = a(5 - 7)² - 4
8 = a(-2)² - 4
+4 +4
12 = 4a
÷4 ÷4
a = 3
It means the equation of the parabola in vertex form:
f(x) = 3(x - 7)² - 4
