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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17024 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.07737660757502, 7.07737660757502. Here's your graph:

RELATED QUESTIONS
A person standing close to the edge on the top of a 170 foot building throws a baseball... (answered by KMST)

A person standing close to the edge on the top of a 264 foot building throws a baseball... (answered by KMST)

A person standing close to the edge on the top of a 195-foot building throws a baseball... (answered by Alan3354)

A person standing close to the edge on the top of a 270-foot building throws a baseball... (answered by Alan3354)

A person standing close to the edge on top of a 192-foot building throws a baseball... (answered by nerdybill)

I am not sure if I'm doing this right... I got 2 seconds ? A person standing close to... (answered by jim_thompson5910)

a preson standing close to the edge on the top of a building throws a baseball vertically (answered by stanbon)

A person standing close to the edge on top of a 112-foot building throws a ball... (answered by ikleyn)

A person standing close to the edge on the top of a 160-foot building throws a baseball... (answered by ikleyn,richwmiller)