Answer:
Step-by-step explanation:
The vertex form of an equation of the parabola:
f(x) = a(x - h)² + k
vertex is (-2, -6) so h = -2, k = -6
so:
f(x) = a(x - (-2))² + (-6)
f(x) = a(x + 2)² - 6
the parabola goes through the point (-4, -7) so for x=-4, f(x)=-7
-7 = a(-4+2)² - 6
-7 +6 = a(-2)² - 6 +6
- 1 = a(4)
a = -¹/₄
Therefore the equation of the parabola in vertex form:
f(x) = -¹/₄(x + 2)² - 6
