Answer:
f(x) = -²/₄₉(x - 2)² + 4
Step-by-step explanation:
The vertex form of an equation of the parabola:
f(x) = a(x - p)² + q
vertex is (2, 4) so p = 2, q = 4
so:
f(x) = a(x - 2)² + 4
the parabola goes through the point (-5, 2) so x=-5, f(x)=2
2 = a(-5-2)² + 4
- 2 = a(49)
a = -²/₄₉
Therefore the equation of the parabola in vertex form:
f(x) = -²/₄₉(x - 2)² + 4
