Answer:
f(x) = - 3(x + 8)² + 2
Step-by-step explanation:
f(x) = a(x - h)² + k - the vertex form of the quadratic function with vertex (h, k)
the axis of symmetry at x = -8 means h = -8
the maximum height of 2 means k = 2
So:
f(x) = a(x - (-8))² + 2
f(x) = a(x + 8)² + 2 - the vertex form of the quadratic function with vertex (-8, 2)
The parabola passing through the point (-7, -1) means that if x = -7 then f(x) = -1
so:
-1 = a(-7 + 8)² + 2
-1 -2 = a(1)² + 2 -2
-3 = a
Threfore:
The vertex form of the parabola which has an axis of symmetry at x = -8, a maximum height of 2, and passes through the point (-7, -1) is:
f(x) = -3(x + 8)² + 2
