Ahalf ball is hit with an initial vertical veolicty of 68 ft/sec. the function h=-16t^2+68t models the height h (in feet) of the golf ball at time t (in seconds). does the golf ball reach a height of 70ft? if so what time? what is the maximum height the ball reaches?

Yes; at 1.75 s; 72.25 ft

Step-by-step explanation:

h = -16t² +68t

a = -16; b = 68; c = 0

The vertex h of a parabola is at

h  = -b/(2a) and the maximum height is at

y = f(h)

1. Time to maximum height

2. Maximum height

3. Does the golf ball reach 70 ft?

Yes, it passes 70 ft on the way to its maximum height of 72.25 ft.

4. Time to 70 ft

      -16t² + 68t = 70

-16t² + 68t - 70 = 0

   8t² -34t + 35 = 0

  ( 4t -7) (2t - 5) = 0

4t - 7 = 0          2t - 5 = 0

    4t = 7                2t = 5

      t = 1.75 s          t = 2.5 s

The golf ball reaches 70 ft at 1.75 s on the way up and 2.5 s on the way down.

The diagram below shows the path of your parabola.