SOLUTION: The height of a particular object can be given by the equation h= -16t^2+32t. What is t when h was 12 feet?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height of a particular object can be given by the equation h= -16t^2+32t. What is t when h was 12 feet?      Log On


   

Question 917427: The height of a particular object can be given by the equation h= -16t^2+32t. What is t when h was 12 feet?
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
h = -16t^2+32 t
when h= 12
12 = -16t^2+32 t
subtract 12 on both sides
12-12 =-16t^2+32t-12
0 =-16t^2+32t-12
solve the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case -16t%5E2%2B32t%2B-12+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2832%29%5E2-4%2A-16%2A-12=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+256+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%2832%29%2Bsqrt%28+256+%29%29%2F2%5C-16+=+0.5
t%5B2%5D+=+%28-%2832%29-sqrt%28+256+%29%29%2F2%5C-16+=+1.5

Quadratic expression -16t%5E2%2B32t%2B-12 can be factored:
-16t%5E2%2B32t%2B-12+=+-16%28t-0.5%29%2A%28t-1.5%29
Again, the answer is: 0.5, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B32%2Ax%2B-12+%29

so t is 0.5 &1.5