SOLUTION: Please I need help solving the following problem. Suppose you hit a ball and the path of it's path follows the graph f(x)= -16x^2 +20x +3. How many seconds will it take for the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please I need help solving the following problem. Suppose you hit a ball and the path of it's path follows the graph f(x)= -16x^2 +20x +3. How many seconds will it take for the       Log On


   

Question 696680: Please I need help solving the following problem.
Suppose you hit a ball and the path of it's path follows the graph f(x)= -16x^2 +20x +3. How many seconds will it take for the ball to hit the ground? Round the answer to nearest second.
A method I was using to find the roots of the equation was to multiply ac, -16(3) = -48, so that way I try finding the factors of -48 that sum up to 20 so these factors can be used in the bionomials that create a product of the equation above--but it was here where I got confused. If there's another method to solve the roots of f(x)= -16x^2 +20x +3, that would be really helpful.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you hit a ball and the path of it's path follows the graph f(x)= -16x^2 +20x +3. How many seconds will it take for the ball to hit the ground? Round the answer to nearest second.
A method I was using to find the roots of the equation was to multiply ac, -16(3) = -48, so that way I try finding the factors of -48 that sum up to 20 so these factors can be used in the bionomials that create a product of the equation above--but it was here where I got confused. If there's another method to solve the roots of f(x)= -16x^2 +20x +3, that would be really helpful.
-----------------
You're taking the right approach. It hits the ground when f(x) = 0
f(x)= -16x^2 +20x +3 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B20x%2B3+=+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=%2820%29%5E2-4%2A-16%2A3=592.

Discriminant d=592 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-20%2B-sqrt%28+592+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+592+%29%29%2F2%5C-16+=+-0.135345316287277
x%5B2%5D+=+%28-%2820%29-sqrt%28+592+%29%29%2F2%5C-16+=+1.38534531628728

Quadratic expression -16x%5E2%2B20x%2B3 can be factored:
-16x%5E2%2B20x%2B3+=+%28x--0.135345316287277%29%2A%28x-1.38534531628728%29
Again, the answer is: -0.135345316287277, 1.38534531628728. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B20%2Ax%2B3+%29

----------------
Ignore the negative solution.