Question

a rocket is launched in the air. its height in feet is given by h = -16t² + 16t where t represents the time in seconds after launch. interpret the coordinates of the vertex in context. answer attempt 1 out of 2 the x - coordinate (or t - coordinate) of the vertex is and represents the y - coordinate (or h - coordinate) of the vertex is and represents

Explanation:

Step1: Recall vertex - t formula

For a quadratic function $h(t)=at^{2}+bt + c$, the $t$ - coordinate of the vertex is given by $t=-\frac{b}{2a}$. In the function $h(t)=-16t^{2}+16t$, $a=-16$ and $b = 16$.

Step2: Calculate t - coordinate of vertex

$t=-\frac{16}{2\times(-16)}=\frac{16}{32}=0.5$. This represents the time in seconds after launch when the rocket reaches its maximum height.

Step3: Calculate h - coordinate of vertex

Substitute $t = 0.5$ into the function $h(t)=-16t^{2}+16t$. So $h(0.5)=-16\times(0.5)^{2}+16\times0.5=-16\times0.25 + 8=-4 + 8=4$. This represents the maximum height of the rocket in feet.

Answer:

The x - coordinate (or t - coordinate) of the vertex is $0.5$ and represents the time in seconds after launch when the rocket reaches its maximum height.
The y - coordinate (or h - coordinate) of the vertex is $4$ and represents the maximum height of the rocket in feet.