Question

The equation below can be used to determine , the height in feet of a model rocket seconds after it is launched from a roof that is 48 feet in height.

h= -16t^2+128t+48
Which equation reveals the maximum height reached by the model rocket?

Answer 1

To find the maximum height reached by the model rocket, we need to determine the vertex of the quadratic function given by the equation h= -16t^2+128t+48. The vertex of the quadratic function occurs at the point (t,h) given by:

t = -b/2a, and h = f(t)

where a = -16, b = 128, and c = 48. Plugging in the values, we get:

t = -128/(2*(-16)) = 4 seconds

To find the maximum height, we substitute t = 4 seconds back into the equation:

h = -16(4)^2 + 128(4) + 48 = 256 feet

Therefore, the equation that reveals the maximum height reached by the model rocket is:

h = 256 feet.