A fountain shoots water from a nozzle at its base. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by the function h(t) = –16t2 + 17t + 8. What is the maximum height of the water? Round to the nearest tenth.
______________ft
recall that in the general quadratic, max y occurs at x = -b/2a. In this case, when t = 17/32.
Just plug that in to get maximum h.
801/64
To find the maximum height of the water, we need to determine the vertex of the equation. The vertex represents the highest point on the graph, which in this case corresponds to the maximum height.
The equation for the height of the water is h(t) = -16t^2 + 17t + 8.
To find the vertex, we use the formula t = -b/(2a), where a = -16 (the coefficient of t^2) and b = 17 (the coefficient of t).
Substituting the values into the formula, we get:
t = -17/(2*(-16))
t = -17/(-32)
t = 0.53125
Now that we have the value of t, we can substitute it back into the original equation to find the value of h(t):
h(t) = -16(0.53125)^2 + 17(0.53125) + 8
h(t) = -16(0.28203) + 9.035 + 8
h(t) ≈ 17.5
Therefore, the maximum height of the water is approximately 17.5 ft.