a ball is thrown vertically upward. after (t) seconds, its height (h) (in feet) is given by the function…

a ball is thrown vertically upward. after (t) seconds, its height (h) (in feet) is given by the function (h(t)=88t - 16t^{2}). after how long will it reach its maximum height? do not round your answer. time: seconds

a ball is thrown vertically upward. after (t) seconds, its height (h) (in feet) is given by the function (h(t)=88t - 16t^{2}). after how long will it reach its maximum height? do not round your answer. time: seconds

Answer

Answer:

$\frac{11}{4}$

Explanation:

Step1: Identify the quadratic - function form

The height function is $h(t)=- 16t^{2}+88t$, which is in the form $y = ax^{2}+bx + c$ where $a=-16$, $b = 88$, $c = 0$.

Step2: Use the formula for the vertex of a parabola

The $t$ - value of the vertex of a parabola $y = ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$.

Step3: Substitute the values of $a$ and $b$

Substitute $a=-16$ and $b = 88$ into the formula: $t=-\frac{88}{2\times(-16)}=\frac{88}{32}=\frac{11}{4}$.