The object will reach a height of 90ft
To solve this exercise we are going to use the discriminant of the quadratic polynomial ax²+bx+c=0, which is b²-4ac.
If the discriminant is negative, then there are no real solutions to the equation.
If the discriminant is zero, there is only one solution.
If the discriminant is positive, there are two real solutions.
We have the equation h(t)=18t-16t² which describes the model of the height h (feet) reached in t (seconds) by an object propelled straight up from the ground at a speed of 80 ft/s. We want to use the discriminant to find whether the object will ever reach a height of 90ft.
First, we have to rewrite the equation to the form ax²+bx+c=0 and we know the height that is possible to reach for the object h=90ft.
90 = 80t-16t² ----------> -16t²+80t-90=0
Using the discriminan equation D = b²- 4ac.
From the quadratic polynomial -16t²+80t-90=0, we have a = -16, b = 80, and c = -90
D = (80)² - 4 (-16)(-90)
D = 6400 - 5760 = 640
Since the discriminant D is positive, the object will reach a height of 90ft.