Problem PageA ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 120t - 16t^2 . After how long will it reach its maximum height?Do not round your answer.

Accepted Solution

Answer:  After 3.75 secondsStep-by-step explanation:  For a Quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex], if [tex]a<0[/tex] then the parabola opens downward. Rewriting the given function as: [tex]h(t) = - 16t^2+120t[/tex] You can identify that [tex]a=-16[/tex] Since [tex]a<0[/tex] the the parabola opens downward. Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can  find it with this formula: [tex]t=\frac{-b}{2a}[/tex] Substitute values, we get [tex]t=\frac{-120}{2(-16)}=3.75\ seconds[/tex]