pre-calculus, urgent, ball vertically thrown upward

Question

A ball is thrown vertically upward with an initial velocity of feet per second. The distance s​ (in feet) of the ball from the ground after t seconds is s = 96t - 16t^2

​The ball will strike the​ ground at 6 seconds.

The ball is more than 140 feet above the ground for the time t when: ____ < t < ______

Answer 1

Abigail

You can draw the function on Desmos or a graphing calculator (y = 96x - 16x^2).

Then also draw y = 140.

See where the two lines intersect.

The x coordinates of those points are what you need.

Alternatively solve 96t - 16t² = 140

16t² - 96 t + 140 = 0

4t² - 24t + 35 = 0

(2t-7) (2t-5) = 0

t = 3.5 or 2.5

As the function is facing upwards (a < 0), your required t range will be 2.5 < t < 3.5