A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What is the maximum height that the ball will reach?Do not round your answer.

Accepted Solution

Answer: 42.25 feetStep-by-step explanation: We know that after "t" seconds, its height "h" in feet is given by this function: [tex]h(t) = 52t -16t^2[/tex] The maximum height is the y-coordinate of the vertex of the parabola. Then, we can use the following formula to find the corresponding value of "t" (which is the x-coordinate of the vertex): [tex]x=t=\frac{-b}{2a}[/tex] In this case: [tex]a=-16\\b=52[/tex] Substituting values, we get : [tex]t=\frac{-52}{2(-16)}\\\\t=1.625[/tex] Substituting this value into the function to find the maximum height the ball will reach, we get: [tex]h(1.625) = 52(1.625) -16(1.625)^2\\\\h(1.625) =42.25\ ft[/tex]