Question

PLEEEASE HELP ME

Answer 1

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