Question

4. The equation h = -16t² + 20t + 19 gives the height h, in feet, of a ball as a function of time t, in seconds,

after it is kicked. What is the maximum height the ball reaches?

Answer 1

h=16(t+5/8)^2+51/4

h=25.25

Answer 2

The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:

t = -b/2a

where a = -16 and b = 20. Substituting these values, we get:

t = -20 / (2 * -16) = 0.625 seconds

To find the maximum height, we can substitute this value of t back into the original equation:

h = -16(0.625)^2 + 20(0.625) + 19

h = -6.25 + 12.5 + 19

h = 25.25 feet

Therefore, the maximum height the ball reaches is 25.25 feet.