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 $h = -16t^2 + 64t$, 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 64 ft.
b) estimate the time when the fireball is at its maximum height.
the time when the fireball is at its maximum height is $t = \square$ sec.

Explanation:

Step1: Identify vertex formula for parabola

For quadratic $h(t)=at^2+bt+c$, vertex time is $t=-\frac{b}{2a}$

Step2: Substitute a=-16, b=64

$t=-\frac{64}{2\times(-16)}$

Step3: Calculate the value

$t=-\frac{64}{-32}=2$

Answer:

2