Answer:
A: at 3/4, or 0.75 seconds
B: 81 feet
C: 3 seconds
Step-by-step explanation:
Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.
The general form for a quadratic equation is ax² + bx + c,
Our equation is h(t) = -16t² + 24t + 72
here a is -16, and b is 24
To find the x coordinate of the vertex, use x = -b/(2a)
We have x = -24/[2(-16)]
x = -24/-32
x = 3/4
So at 3/4 seconds, the ball reaches is maximum height
Now plug that into the equation to find the y value, which will be the height...
y = -16(3/4)² + 24(3/4) + 72
y = -16(9/16) + 72/4 + 72
y = -9 + 18 + 72
y = 81 feet
To see how long it took to reach ground, solve the equation..
0 = -16t² + 24t + 72
0 = 2t² - 3t - 9 (divide both sides by -8)
0 = (2t + 3)(t - 3)
so 2t + 3 = 0,
t = -3/2 *this answer is ignored because t is time,so it must be positive
and t - 3 = 0
t = 3
, or 7.4 meters per second