A ball is shot out of a cannon at ground level, We know that its height H in feet after t sec given by the function H(t) 144t-16t Com is a. Find H(3), H(6), H(4), and H(5). Why are some of the outputs equal? H(3) feet

Answer:H(3) = 288 feetH(4) = 320 feetH(5) = 320 feetH(6) = 288 feetStep-by-step explanation:A ball is shot out of a cannon at ground level so the ball will follow a parabolic path.Since height H and time t of the ball have been described by a function H(t) = 144t - 16t²Then we have to find the values of H(3), H(4), H(5) and H(6).H(3) = 144×3 - 16(3)²        = 432 - 144        = 288 feetH(4) = 144×4 - 16(4)²        = 576 - 256        = 320 feetH(5) = 144×5 - 16(5)²        = 720 - 400        = 320 feetH(6) = 144×6 - 16(6)²        = 864 - 576        = 288 feetHere we are getting the value like H(3), H(6) and H(4), H(5) are same because in a parabolic path ball first increase in the height above the ground then after the maximum height it decreases.Therefore, after t = 3 and t = 6 heights of the canon ball are same. Similarly after t = 4 and t = 5 heights of the canon above the ground are same.