Justin launches a water balloon vertically from a platform on his roof. The height of the balloon (in feet) is represented by

Question

Justin launches a water balloon vertically from a platform on his roof. The height of the balloon (in feet) is represented by the equation h=-16t^2+32t+48 where t is the time (in seconds) after he launches the water balloon.

What is the maximum height of the water balloon?

How long does it take the water balloon to reach its maximum height?

Select two answers: one for each question.

Answer 1

The equation: h(t) = -16t² + 32t + 48 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 (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 = 64 feet

ANSWER: h_max = 64 feet

To find the time for the balloon to reach this height, solve: 64 = -16t² + 32t + 48

Subtract 64 from both sides of the equation: 0 = -16t² + 32t -16

Rearrange and Factor: -16(t² -2t +1) = 0

-16(t - 1)(t - 1) = 0

t - 1 = 0; t = 1 sec

ANSWER: time to get to the maximum height = 1 sec