A flare is launched from a boat. The height, h, in meters, of the flare above the water is approximately modelled by the function h(t) = -15t2 + 150t, where t is the number of seconds after the flare is launched. What is the highest point that the flare reaches?

Answer 1

To find the highest point that the flare reaches, we need to find the maximum value of the function h(t)=-15t^2 + 150t.

To do this, we first need to find the vertex of the parabolic function. The vertex of a parabolic function of the form h(t) = at^2 + bt + c is given by the formula t = -b/2a.

In this case, a = -15 and b = 150, so the vertex of the function h(t) is at t = -150/(2*(-15)) = -150/-30 = 5 seconds.

To find the maximum height reached by the flare, we substitute t = 5 into the function h(t):

h(5) = -15(5)^2 + 150(5) = -15(25) + 750 = -375 + 750 = 375

Therefore, the highest point that the flare reaches is 375 meters above the water.