Answer:
f(x) = -3(x + 4)² - 6
Step-by-step explanation:
The vertex form of an equation of the parabola:
f(x) = a(x - h)² + k
the vertex is (-4, -6) ⇒ h = -4, k = -6
so:
f(x) = a(x - (-4))² + (-6)
f(x) = a(x + 4)² - 6
The parabola goes through the point (1, -81) ⇒ x=1, f(x)=-81
-81 = a(1 + 4)² - 6
-81 = a(5)² - 6
+6 +6
-75 = 25a
÷25 ÷25
a = -3
Therefore the equation of the parabola in vertex form:
f(x) = -3(x + 4)² - 6
