SOLUTION: During practice, a softball pitcher throws a ball whose height can be modeled by the equation h=-16t^2+24t+1, where h=height in feet and t=time in seconds. How long does it take fo

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Question 720438: During practice, a softball pitcher throws a ball whose height can be modeled by the equation h=-16t^2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
During practice, a softball pitcher throws a ball whose height can be modeled by the equation h=-16t^2+24t+1, where h=height in feet and t=time in seconds. How long does it take for the ball to reach a height of 6 feet?
.
Set h to 6 and solve for t:
h=-16t^2+24t+1
6=-16t^2+24t+1
0 = -16t^2+24t-5
0 = 16t^2-24t+5
solve the above using the "quadratic formula" which yields:
t = {0.25, 1.25}
The ball reaches the height of 6 feet "on the way up" at
0.25 seconds
and again, "on the way down" at
1.25 seconds
.
Details of quadratic follows:

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=256 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.25, 0.25. Here's your graph: