SOLUTION: You are jumping off the 12-foot diving board at the manicipal pool. You bounce up at 6 feet per second and drop to the water. Your height h (in feet) above the water in terms of t

Algebra ->  Square-cubic-other-roots -> SOLUTION: You are jumping off the 12-foot diving board at the manicipal pool. You bounce up at 6 feet per second and drop to the water. Your height h (in feet) above the water in terms of t       Log On


   

Question 1028734: You are jumping off the 12-foot diving board at the manicipal pool. You bounce up at 6 feet per second and drop to the water. Your height h (in feet) above the water in terms of t seconds is given by h(t)=-16t^2+6t+12.

a.) when do hit the water? round your answer to the nearest hundredth.

b.) what is your maximum height above the pool?

Thank you so much for taking your time to help me!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-16t%5E2+%2B+6t+%2B+12+
(a)
You hit the water when +h%28t%29+=+0+, which
is 12 ft below the diving board
+0+=+-16t%5E2+%2B+6t+%2B+12+
you can use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-16+
+b+=+6+
+c+=+12+
+t+=+%28-6+%2B-+sqrt%28+6%5E2+-+4%2A%28-16%29%2A12+%29%29+%2F+%282%2A%28-16%29%29+
+t+=+%28-6+%2B-+sqrt%28+36+%2B+768+%29%29+%2F+%28-32%29+
+t+=+%28-6+%2B-+sqrt%28+804+%29%29+%2F+%28-32%29+
+t+=+%28-6+-+28.3549+%29+%2F+%28-32%29+
+t+=+%28+-34.3549+%29+%2F+%28+-32+%29+
+t+=+1.0736+
You hit the water in 1.07 sec
----------------------------
(b)
The maximum height is when:
+t%5Bmax%5D+=+-b%2F%282a%29+
+t%5Bmax%5D+=+-6%2F%282%2A%28-16%29+%29+
+t%5Bmax%5D+=+3%2F16+
Plug this back into equation
+h%28t%29+=+-16t%5E2+%2B+6t+%2B+12+
+h%5Bmax%5D+=+-16%2A%283%2F16%29%5E2+%2B+6%2A%283%2F16%29+%2B+12+
+h%5Bmax%5D+=+-.5625+%2B+1.125+%2B+12+
+h%5Bmax%5D+=+12.5625+
The maximum height above the pool is 12.56 ft
------------------
check:
here's the plot:
+graph%28+400%2C+400%2C+-2%2C+2%2C+-3%2C+16%2C+-16x%5E2+%2B+6x+%2B+12+%29+