Answer :
Answer:
f(x) = - 2(x - 4)² + 1
Step-by-step explanation:
f(x) = a(x - h)² + k - the vertex form of an equation of a parabola with vertex (h, k)
(4, 1) ⇒ h = 4. k = 1
f(x) = a(x - 4)² + 1 - the vertex form of an equation of the parabola with vertex (4, 1)
the parabola passes through (7, -17) ⇒ x=7, f(x)=-17
-17 = a(7 - 4)² + 1
-17 -1 = a(3)² + 1 -1
-18 = 9a
a = -2
The equation of the parabola in vertex form that passes through (7, -17) and has a vertex (4, 1):
f(x) = -2(x - 4)² + 1