Theo's flying disc got stuck in a tree 14 feet from the ground. theo threw his shoe up at the disc to dislodge it. the height in feet h of the shoe is given by the equation h= -16^2+25t+6, where t is the time in seconds. determine whether the shoe hit the disc. use the discriminant to explain your answer.

The shoe hit the disc.

Step-by-step explanation:

Let be a quadratic function where a, b and c are the real coefficients of the function.

Then the discriminant of the function is:

The result of this expression gives us information about the roots of this equation.

* If the discriminant is > 0 then the equation has 2 real solutions

* If the discriminant is > 0 then the equation has 2 complex solutions

* If the discriminant is = 0 then the equation has 1 real solution.

For this case we have the equation:

If we assume that the shoe reached the disc, then

So:

Then the discriminant is:

The discriminant is greater than 0. Then the equation has 2 real solutions. and .

This means that if there are values of t for which . In other words, this means that the shoe reached the disc.

In fact if you use the quadratic formula to solve the equation you will get:

the answer is n