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A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81

. Which of the following statements is true?

The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.

The airplane reaches its maximum height of 12 feet in 81 seconds.

Sagot :

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The statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

Since the height of the plane is a function given by a parabola, we need to know the equation of a parabola in vertex form

What is the equation of a parabola in vertex form?

The equation of a parabola with vertex (h,k) is given by y = a(x - h) + k

Since the height (in feet) of the airplane as a function of time (in seconds after the timer was started) is given by the equation h(t) = −(t − 12) + 81

  • Since this is the equation of a parabola in vertex form, comparing h with y, we have that a = -1, h = 12 and k = 81
  • Since a = -1 < 0 this implies that the point (h, k) = (12, 81) is a maximum point

So, the statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

Learn more about equation of a parabola in vertex form here:

https://brainly.com/question/17684824

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