Question

Fireworks are fired from the rode of a 100-foot building. The equation h= -16t2+84t + 100 models the height, h, of the fireworks at any given time t, How high do the fireworks get?

Answer 1

The fireworks reach a maximum height of 256 feet, which is determined by finding the vertex of the parabola represented by the quadratic equation modeling the fireworks' height as a function of time.

Step-by-step explanation:

To find out how high the fireworks get, we need to determine the maximum value of the quadratic equation h = -16t2 + 84t + 100. This equation models the height (h) of the fireworks at any given time (t). To find the maximum height, we need to find the vertex of the parabola represented by the quadratic equation. The time at which the fireworks reach maximum height (tvertex) is given by tvertex = -b/(2a), where a is the coefficient of t2 and b is the coefficient of t. In this equation, a = -16 and b = 84, so tvertex = -84/(2 × -16) = 2.625 seconds.

Plugging tvertex back into the original equation gives us the maximum height (hmax): hmax = -16 × (2.625)2 + 84 × 2.625 + 100. After doing the calculations, we find that the maximum height hmax = 256 feet. So, the fireworks get up to 256 feet high before starting to fall back down.