SOLUTION: A batter hits a baseball and runs toward first base. Lorenzo runs toward the ball to catch it before it hits the ground. Ignoring wind resistance, the equation h(t)=-16t^2+42t+3.

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Question 408890: A batter hits a baseball and runs toward first base. Lorenzo runs toward the ball to catch it before it hits the ground. Ignoring wind resistance, the equation h(t)=-16t^2+42t+3.5 can be used to find h, the height of the ball in feet, using t, the time in seconds after it is hit. How many seconds after the ball is hit does Lorenzo have before the ball hits the ground?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
h(t)=-16t^2+42t+3.5
set h(t) to zero and solve for t:
0=-16t^2+42t+3.5
apply the quadratic formula to give us:
t = {-0.08, 2.71}
we can throw out the negative solution leaving us with:
t = 2.71 seconds
.
details of quadratic formula 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=1988 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.0808435506004972, 2.7058435506005. Here's your graph:

= 0