The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 40t + 2. From what height was the balloon released?
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Step-by-step explanation:
The equation: h(t) = -5t2 + 40t + 2. is the position or height equation. It is the equation of a parabola. Since the leading coefficient -16 is negative, we have a parabola that has a maximum (a vertex is the highest point).
The easiest way to find the maximum height is to find the vertex since the y-value of the vertex is the maximum height. When the equation is in the form Ax2 + Bx + C = 0, the vertex is (-B/(2A), h(-B/(2A))).
-B/(2A) = -32/(2*-16) = -32/-32 = 1
h(1) = -16(1)2 + 32(1) + 48 = 2 feet
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