Respuesta :
Answer:
A: Â at 3/4, or 0.75 seconds
B: Â 81 feet
C: Â 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. Â
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
Â
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 Â
   y = -16(9/16) + 72/4 + 72
      y = -9 + 18 + 72
Â
        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, Â
         t = -3/2   *this answer is ignored because t is time,so it must be positive
       and  t - 3 = 0
            t = 3
