Question

The quadratic equation y = - 16t^2+ 56t+ 2 represents the height of a projectile,

y, in feet, at a particular time, t, in seconds.
For what interval or intervals of time will the projectile be above 26 feet?

Answer 1

0.5 < x < 3

or (0.5, 3)

Explanation:

-16t² + 56t + 2 = 26

Subtract both sides by 26

-16t² + 56t + 2 = 26

-26 -26

-16t² + 56t - 24 = 0

Divide both sides by -8 to simplify

(-16t² + 56t - 24)/8 = 0/8

2t² - 7t + 3 = 0

Factor

(x - 3)(2x - 1) = 0

Do this to find the x's

x - 3 = 0

+ 3 +3

x = 3

2x - 1 = 0

+ 1 + 1

2x = 1

2x/2 = 1/2

x = 0.5

0.5 < x < 3

This means the intervals will have to be between 0.5 and 3 seconds