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Answer :
By understading quadratic equations in vertex form, the toy rocket reaches its maximum height as t = 4 seconds.
How to find the time when a toy rocket reaches its maximum height
In this question we find the function for the height of the rocket in the form of a quadratic equation as function of time. We can find the time when maximum height is reached by transforming quadratic equation from standard form into vertex form, since it is represented graphically by the vertex of a parabola.
First, write the quadratic equation:
h(t) = - 16 · t² + 128 · t
Second, complete the square:
h(t) = - 16 · (t² - 8 · t)
h(t) - 16 · 16 = - 16 · (t² - 8 · t + 16)
h(t) - 256 = - 16 · (t - 4)²
Third, find the time associated with the maximum height:
t = 4
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