SOLUTION: #1. A person standing close to the edge on the top of a 122-foot building throws a baseball vertically upward. The quadratic equation h = -16 t^2 + 96 t + 122 models the b

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Question 831087: #1.
A person standing close to the edge on the top of a 122-foot building throws a baseball vertically upward. The quadratic equation
h = -16 t^2 + 96 t + 122
models the ball's height h above the ground in feet, t seconds after it was thrown.
How high is the ball after 3 seconds?


How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
#1.
A person standing close to the edge on the top of a 122-foot building throws a baseball vertically upward. The quadratic equation
h = -16 t^2 + 96 t + 122
models the ball's height h above the ground in feet, t seconds after it was thrown.
How high is the ball after 3 seconds?
set t=3 and solve:
h = -16*3^2 + 96*3 + 122
h = -16*9 + 96*3 + 122
h = -144 + 288 + 122
h = 144 + 122
h = 266 feet
How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.
set h=0 and solve for t:
0 = -16t^2 + 96 t + 122
solve using the quadratic formula to get:
t={-1.1, 7.1}
throw out the negative solution (extraneous) leaving:
t = 7.1 seconds
.
Details of quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B96x%2B122+=+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=%2896%29%5E2-4%2A-16%2A122=17024.

Discriminant d=17024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-96%2B-sqrt%28+17024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2896%29%2Bsqrt%28+17024+%29%29%2F2%5C-16+=+-1.07737660757502
x%5B2%5D+=+%28-%2896%29-sqrt%28+17024+%29%29%2F2%5C-16+=+7.07737660757502

Quadratic expression -16x%5E2%2B96x%2B122 can be factored:
-16x%5E2%2B96x%2B122+=+-16%28x--1.07737660757502%29%2A%28x-7.07737660757502%29
Again, the answer is: -1.07737660757502, 7.07737660757502. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B96%2Ax%2B122+%29