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?
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.