Matthew launches a ball at 34 meters/sec from a 28 meter tall platform. The function of the ball's height (h) at time (t) seconds after launch is h (t) = - 2t^2+34t+28. Determine how long it will take for the ball to be at its original height.

17 seconds

Step-by-step explanation:

h (t) represents height, we want to know when the ball will return to a height of 28 feet. So our equation is ...

28 = - 2t² + 34t + 28

Now solve for t ...

0 = - 2t² + 34t (subtract 28 from both sides)

0 = t² - 17t (divide both sides by - 2)

0 = t (t - 17) (factor out a t)

So

t = 0

or

t - 17 = 0

t = 17

0 seconds is the initial height. At 17 seconds, the ball will return to that height