Answer:
f(x) = -8(x + 2)² + 5
Explanation:
y = a(x - p)² + q - the vertex form of an equation of a parabola with a vertex (p, q)
(-2, 5) ⇒ p = -2, q = 5
y = a(x + 2)² + 5 - the vertex form of an equation of the parabola with vertex (-2, 5)
y-intercept of -27 means x=0, y=-27
-27 = a(0 + 2)² + 5
-27 -5 = a(2)² + 5 -5
-32 = 4a
a = -8
The equation of the parabola in vertex form that has a vertex (-2, 5) and y-intercept of -27:
f(x) = -8(x + 2)² + 5