contestada

If a toy rocket is launched vertically upward from the ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation:
h(t) = -16t^2 + 128t
What is the maximum height the rocket reaches?

Respuesta :

Ashraf82

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 = [tex]\frac{-b}{2a}[/tex] 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 = [tex]\frac{-128}{2(-16)}[/tex] = [tex]\frac{-128}{-32}[/tex]

∴ 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

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