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)=120t - 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)=120t - 16t^2. after how long will it reach its maximum height? do not round your answer. time: seconds

Answer

Explanation:

Step1: Identify the function type

The height - function $h(t)=120t - 16t^{2}$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 120$, 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 $b = 120$ into the formula: $t=-\frac{120}{2\times(-16)}$.

Step3: Simplify the expression

First, calculate the denominator: $2\times(-16)=-32$. Then, $t=\frac{120}{32}=\frac{15}{4}$.

Answer:

$\frac{15}{4}$