the height 1 seconds after a toy rocket is launched straight up can be modeled by the function h(t) =-16t^2+23.8t 5, where h(t) is in feet. find the maximum height of the rocket .

Answer 1

I'm going to assume the function h(t) is h(t) = -16t² + 23.8t + 5 (you are missing an operation symbol between the 2nd and 3rd terms) and I'm going to assume that you meant to say "the height "t" seconds after a toy rocket is launched . . . "

h(t) = -16t² + 23.8t + 5 forms the shape of a parabola with a maximum at the vertex. There are several ways to find the vertex, but a fairly straight forward way is to use the fact that for y = ax² + bx + c, the x-coordinate of the vertex is x = -b/(2a). In this case that means t = -23.8/(2•(-16)) = -23.8/-32 = 0.74375 seconds

The height then can be calculated by plugging in t = 0.74375 seconds:

h(0.74375) = -16(0.74375)² + 23.8(0.74375) + 5

h(0.74375) = - 8.850625 + 17.70125 + 5

h(0.74375) = 13.850625 feet