SOLUTION: Sharice hit a baseball, and the flight of the ball was modeled by the following equation: {{{ h = -16t2 + 62t + 4 }}}. After how many seconds will the ball fall to the ground if

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Question 871192: Sharice hit a baseball, and the flight of the ball was modeled by the following equation:
+h+=+-16t2+%2B+62t+%2B+4+. After how many seconds will the ball fall to the ground if it is not caught? Round your answer to the nearest tenth.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-16t2+%2B+62t+%2B+4+.
t = 3.93847632419777 sec 0r 3.9sec (Rounded to the nearest tenth)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B62x%2B4+=+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=%2862%29%5E2-4%2A-16%2A4=4100.

Discriminant d=4100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-62%2B-sqrt%28+4100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2862%29%2Bsqrt%28+4100+%29%29%2F2%5C-16+=+-0.0634763241977652
x%5B2%5D+=+%28-%2862%29-sqrt%28+4100+%29%29%2F2%5C-16+=+3.93847632419777

Quadratic expression -16x%5E2%2B62x%2B4 can be factored:
-16x%5E2%2B62x%2B4+=+-16%28x--0.0634763241977652%29%2A%28x-3.93847632419777%29
Again, the answer is: -0.0634763241977652, 3.93847632419777. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B62%2Ax%2B4+%29