Answer:
Since [tex]f(25\,ft) < 8\,ft[/tex], then we conclude that it will be a goal.
Step-by-step explanation:
Let the trajectory of the ball be represented by [tex]f(x) = -0.05\cdot (x-16)^{2}+11[/tex], where [tex]x[/tex] is the horizontal distance of the ball from origin, in feet, and [tex]f(x)[/tex] is the height of the ball above ground, in feet.
If Deshawn does not block Chris's shot, then we should check if shot will be a goal and this condition must be fulfilled:
[tex]f(25\,ft) < 8\,ft[/tex] (1)
If we know that [tex]x = 25\,ft[/tex], then the height of the ball at the start of the goal is:
[tex]f(x) = -0.05\cdot (x-16)^{2}+11[/tex] (2)
[tex]f(x) = 6.95\,ft[/tex]
Since [tex]f(25\,ft) < 8\,ft[/tex], then we conclude that it will be a goal.
