SOLUTION: h = –16t^2 + vt + c The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per secon

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: h = –16t^2 + vt + c The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per secon      Log On


   



Question 747342: h = –16t^2 + vt + c
The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per second, and c is the starting height in feet.
If Adam, who is 6 feet tall, threw his baseball 80 feet per second straight up into the air, which of the following answers is the best estimate of how long it took the ball to come back to the ground?
I think this is the equation, h= -16t^2+80t+6

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
h= -16t^2+80t+6 (is correct)
.
when the ball is on the ground, h is zero. So, set h to zero and solve for t:
0 = -16t^2+80t+6
0 = 16t^2-80t-6
0 = 8t^2-40t-3
solve using the "quadratic formula" yields:
x = {5.07, -0.07}
throw out the negative value (extraneous) leaving
x = 5.07 seconds
.
Details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-40x%2B-3+=+0) has the following solutons:

x%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=%28-40%29%5E2-4%2A8%2A-3=1696.

Discriminant d=1696 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--40%2B-sqrt%28+1696+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1696+%29%29%2F2%5C8+=+5.07390753524675
x%5B2%5D+=+%28-%28-40%29-sqrt%28+1696+%29%29%2F2%5C8+=+-0.0739075352467502

Quadratic expression 8x%5E2%2B-40x%2B-3 can be factored:
8x%5E2%2B-40x%2B-3+=+8%28x-5.07390753524675%29%2A%28x--0.0739075352467502%29
Again, the answer is: 5.07390753524675, -0.0739075352467502. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-40%2Ax%2B-3+%29