Question

The height, in feet, of a t-shirt launched from a t-shirt cannon high in the stands at a football stadium is given by h(x)=-16x^2+64x+80, where x is the time in seconds after the t-shirt is launched. What is the maximum height of the t-shirt and how many seconds does it take to reach the maximum height?

Answer 1

The maximum height of the t-shirt is 144 feet and it takes 2 seconds to reach the maximum height.

Step-by-step explanation:

The maximum height of the t-shirt can be determined by finding the vertex of the parabolic function. In the given equation h(x) = -16x^2 + 64x + 80, the vertex can be found using the formula x = -b/2a, where a = -16 and b = 64. Plugging in these values, we get x = -64/(-32) = 2 seconds.

To find the maximum height, we substitute x = 2 into the equation h(x) = -16x^2 + 64x + 80. Thus, h(2) = -16(2)^2 + 64(2) + 80 = 144 feet.

Therefore, the maximum height of the t-shirt is 144 feet and it takes 2 seconds to reach the maximum height.

Answer 2

max height is 144

take 3 seconds