The height in feet of a diver above the surface of a pool is given by the equation h= -16t^2 +20t +12, where t is the time in seconds after the diver jumps.1. How many seconds after the jumping is the diver’s height 8 meters? 2. How long does it take the diver to reach the water?

#1) 1.4 seconds
#2) 1.7 seconds

For #1, we set the function equal to 8:
8 = -16t² + 20t + 12

To solve a quadratic equation we want it equal to 0, so subtract 8 from both sides:
8 - 8 = -16t² + 20t + 12 - 8
0 = -16t² + 20t + 4

Use the quadratic formula to solve this:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{-20\pm \sqrt{20^2-4(-16)(4)}}{2(-16)}=\frac{-20\pm \sqrt{400--256}}{-32} \\ \\=\frac{-20\pm \sqrt{400+256}}{-32}=\frac{-20\pm \sqrt{656}}{-32} \\ \\=\frac{-20\pm 25.61}{-32}=\frac{-20+25.61}{-32}\text{ or }\frac{-20-25.61}{-32} \\ \\=\frac{5.61}{-32}\text{ or }\frac{-45.61}{-32}=-0.175\text{ or }1.4[/tex]

Since a negative time makes no sense, the answer is 1.4

For #2,
[tex]t=\frac{-20\pm \sqrt{20^2-4(-16)(12)}}{2(-16)}=\frac{-20\pm \sqrt{400--768}}{-32} \\ \\=\frac{-20\pm \sqrt{1168}}{-32}=\frac{-20\pm 34.18}{-32}=\frac{-20-34.18}{-32}\text{ or }\frac{-20+34.18}{-32}=1.7\text{ or }-0.44[/tex]

Since negative time makes no sense, the answer is 1.7.