Question

chloe launches a toy rocket from a platform. the height of the rocket in feet is given by $h(t)=-16t^{2}+24t + 112$ where $t$ represents the time in seconds after launch. how many seconds have gone by when the rocket is at its highest point?

Explanation:

Step1: Identify the function type

The height function $h(t)=- 16t^{2}+24t + 112$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 24$, $c = 112$.

Step2: Use the formula for the vertex of a quadratic

The $t$-coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$.
Substitute $a=-16$ and $b = 24$ into the formula: $t=-\frac{24}{2\times(-16)}$.

Step3: Simplify the expression

First, calculate the denominator: $2\times(-16)=-32$.
Then, $t = \frac{24}{32}=\frac{3}{4}=0.75$.

Answer:

$0.75$