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Answer:
The maximum height of the rocket is 256 feet
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
- (h, k) is the vertex point
- h =
and k = f(h)
- (h, k) is a minimum point if a > 0 and a maximum point if a < 0
Let us use these rules to solve the question
∵ h(t) = -16t² + 128t
→ Compare it by the form of the quadratic function above
∴ a = -16 and b = 128
∵ a < 0
∴ The vertex (h, k) is a maximum point
∴ The maximum height of the rocket is the value of k
→ Use the rule of h above to find it
∵ h = =
∴ h = 4
→ Substitute x in the equation by the value of h to find k
∵ k = h(h)
∴ k = -16(4)² + 128(4)
∴ k = -256 + 512
∴ K = 256
∴ The maximum height of the rocket is 256 feet