Question

Shelly is trying to throw her keys up to her brother Mark who is on a second-floor balcony. The path of the keys can be modeled by the function h(t) = 2t^2 - 16t + 20. Is it possible for Mark to catch the keys if he is catching them at a height of 16 feet?

Answer 1

2t² - 16t + 20 = 16

t² - 8t + 10 = 8

t² - 8t + 16 = 14

(t - 4)² = 14

t - 4 = √14

t = 4 + √14 = about 7.74

Yes, it is possible for Mark.

Answer 2

To determine if Mark can catch the keys at a height of 16 feet, we need to solve a quadratic equation.

Step-by-step explanation:

The given function is a quadratic function that models the path of Shelly's keys. The function is h(t) = 2t^2 - 16t + 20, where h(t) represents the height of the keys at time t.

To determine if Mark can catch the keys when they are at a height of 16 feet, we need to find the value of t when h(t) = 16. So, we set up the equation:

16 = 2t^2 - 16t + 20

Rearranging the equation, we get:

2t^2 - 16t + 4 = 0

This is a quadratic equation. We can find the time t by solving this equation using factoring, completing the square, or using the quadratic formula.

If there is a real solution for t, it means that Mark can catch the keys at a height of 16 feet. If there are no real solutions, it means that Mark cannot catch the keys at that height.