Question

the height h of a fireball launched from a roman candle with an initial velocity of 64 feet per second is given by the equation h = -16t² + 64t, where t is time in seconds after launch. use the graph of this function to answer the questions.\
\
a) estimate the maximum height of the fireball.\
the maximum height of the fireball is \\(\square\\) ft.

Explanation:

Step1: Identify vertex of parabola

The function $h(t) = -16t^2 + 64t$ is a downward-opening parabola. Its vertex (maximum point) occurs at $t = -\frac{b}{2a}$ for $ax^2+bx+c$. Here $a=-16$, $b=64$.
$t = -\frac{64}{2(-16)} = 2$ seconds.

Step2: Calculate max height

Substitute $t=2$ into the height function.
$h(2) = -16(2)^2 + 64(2) = -16(4) + 128 = -64 + 128$

Answer:

64 ft