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)=72t - 16t². 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)=72t - 16t². after how long will it reach its maximum height? do not round your answer. time: seconds

Answer

Explanation:

Step1: Identify the quadratic - function form

The height function is $h(t)=- 16t^{2}+72t$, which is in the form $y = ax^{2}+bx + c$ where $a=-16$, $b = 72$, and $c = 0$.

Step2: Use the formula for the vertex of a quadratic function

The $t$ - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 72$ into the formula: $t=-\frac{72}{2\times(-16)}$.

Step3: Simplify the expression

$t=\frac{72}{32}=\frac{9}{4}$.

Answer:

$\frac{9}{4}$