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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:
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