Solve Using the Quadratic Formula

Question

The function h(t)=-16t²+17t+6 can be used to determine the height, h(t), in feet, of a super ball t seconds after it is thrown upward from a window on the first floor. At what time does the ball reach a height of 2.25 feet above the ground?

Answer 1

2.25 = 2 1/4 = 9/4= -16t^2 +17t +6

-16t^2 +17t +15/4 = 0

use the quadratic formula

t = 17/32 +(1/32)sqr(17^2 +64(15/4))

=(17+sqr(289+240))/32

t = (17 +sqr529)/32

t=(17+23)/32

t = 40/32=5/4= 1.25 seconds

-16(5/4)^2 +17(5/4) + 6

=-25 + 85/4 +24/4

= -25 + 109/4

= 9/4=2.25 feet