Question

a rocket is launched in the air. its height in feet is given by h = -16t^2 + 128t 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 $h = - 16t^{2}+128t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 128$, $c = 0$.

Step2: Recall 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 $t=-\frac{b}{2a}$.

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

Substitute $a=-16$ and $b = 128$ into $t =-\frac{b}{2a}$. We get $t=-\frac{128}{2\times(-16)}$.
First, calculate the denominator $2\times(-16)=-32$. Then, $t=\frac{128}{32}$.

Step4: Simplify the expression

$\frac{128}{32}=4$.

Answer:

4