H (t) = - 5t^2+20t+1

what time does the ball reach the same height it was kicked at again? When does the ball reach its max height? What is the max height?

H (t) = - 5t² + 20t + 1

-5t² + 20t + 1 = 0

t = - (20) + / - √ ((20) ² - 4 (-5) (1))

2 (-5)

t = - 20 + / - √ (400 + 20)

-10

t = - 20 + / - √ (420)

-10

t = - 20 + / - 2√ (105)

-10

t = - 20 + 2√ (105) t = - 20 - 2√ (105)

-10 - 10

t = 2 - 0.2√ (105) t = 2 + 0.2√ (105)

h (t) = - 5t² + 20t + 1

h (2 - 0.2√ (105)) = - 5 (2 - 0.2√ (105)) ² + 20 (2 - 0.2√ (105)) + 1

h (2 - 0.2√ (105)) = - 5 (2 - 0.2√ (105)) (2 - 0.2√ (105)) + 20 (2) - 20 (0.2√ (105)) + 1

h (2 - 0.2√ (105)) = - 5 (4 - 0.4√ (105) - 0.4√ (105) + 0.04√ (11025)) + 40 - 4√ (105) + 1

h (2 - 0.2√ (105)) = - 5 (4 - 0.8√ (105) + 0.04 (105)) + 40 + 1 - 4√ (105)

h (2 - 0.2√ (105)) = - 5 (4 - 0.8√ (105) + 4.2) + 41 - 4√ (105)

h (2 - 0.2√ (105)) = - 5 (4 + 4.2 - 0.8√ (105)) + 41 - 4√ (105)

h (2 - 0.2√ (105)) = - 5 (8.2 - 0.8√ (105)) + 41 - 4√ (105)

h (2 - 0.2√ (105)) = - 5 (8.2) - 5 (-0.8√ (105)) + 41 - 4√ (105)

h (2 - 0.2√ (105)) = - 41 + 4√ (105) + 41 - 4√ (105)

h (2 - 0.2√ (105)) = - 41 + 41 + 4√ (105) - 4√ (105)

h (2 - 0.2√ (105)) = 0 + 0

h (2 - 0.2√ (105)) = 0

(t, h (t)) = (2 - 0.2√ (105), 0)

or

h (t) = - 5t² + 20t + 1

h (2 + 0.2√ (105)) = - 5 (2 + 0.2√ (105)) ² + 20 (2 + 0.2√ (105)) + 1

h (2 + 0.2√ (105)) = - 5 (2 + 0.2√ (105)) (2 + 0.2√ (105)) + 20 (2) + 20 (0.2√ (105)) + 1

h (2 + 0.2√ (105)) = - 5 (4 + 0.4√ (105) + 0.4√ (105) + 0.04√ (11025)) + 40 + 4√ (105) + 1

h (2 + 0.2√ (105)) = - 5 (4 + 0.8√ (105) + 0.04 (105)) + 40 + 4√ (105) + 1

h (2 + 0.2√ (105)) = - 5 (4 + 0.8√ (105) + 4.2) + 40 + 1 + 4√ (105)

h (2 + 0.2√ (105)) = - 5 (4 + 4.2 + 0.8√ (105)) + 41 + 4√ (105)

h (2 + 0.2√ (105)) = - 5 (8.2 + 0.8√ (105)) + 41 + 4√ (105)

h (2 + 0.2√ (105)) = - 5 (8.2) - 5 (0.8√ (105)) + 41 + 4√ (105)

h (2 + 0.2√ (105)) = - 41 - 4√ (105) + 41 + 4√ (105)

h (2 + 0.2√ (105)) = - 41 + 41 - 4√ (105) + 4√ (105)

h (2 + 0.2√ (105)) = 0 + 0

h (2 + 0.2√ (105)) = 0

(t, h (t)) = (2 + 0.2√ (105), 0)