A rock was slung from a sling shot off the top of a building. The height of the rock, relative to theamount of time since leaving the sling shot, can be modeled by a function r (t) where r (t)represents the height of the rock in the feet above ground, and t is the number of seconds since therock left the sling shot.The following equivalent equations represent r (t) in three different forms.r (t) =-16(t 1.75) + 289r(t) D-16 (t- 6) (t + 2.5)r (t) =-16t + 56t + 240Check all of the statements that are true.O the rock hit the ground6 seconds after leaving the sling shot.O the rock hit the ground 2.5 seconds after leaving the sling shot.O The shape of the graph is concave up.O The rock's initial height was 289 feet.O The rock reached its highest point 1.75 seconds after leaving the sling.

The height of the rock,r(t)=-16t-1.752+289r(t)=-16t-6t+2.5r(t)=-16t2+56t+240The height of the rock,r(t)=-16t-1.752+289r(t)=-16t-6t+2.5r(t)=-16t2+56t+240i)the rock hit the ground 6 seconds after leaving the sling shot.Answer: TrueExplanation:when rock hits the ground, its height is 0r(t)=0-16t-6t+2.5=0t-6=0 and t+2.5=0t=6 and t=-2.5time cannot be negativehence t=6ii)the rock hit the ground 2.5 seconds after leaving the sling shot.Answer: Falsebecause,by previous case, the rock hit the ground 6 seconds after leaving the sling shot.iii)The shape of the graph is concave up.Answer: FalseExplanation:r(t)=-16t-1.752+289this is equation of parabola its leading coefficient negative and its opens downeardhence the shape of the graph is concave down.iv)The rock's initial height was 289 feetAnswer: FalseExplanation:at initially time, t=0r(t)=-16t2+56t+240r(0)=-0+0+240=240the rock's initial height was 240 feetv)The rock reached its highest point 1.75 seconds after leaving the slingAnswer: TrueExplanation: r(t)=-16t-1.752+289its vertex point (1.75, 289)here, the graph opens downward, hence it attains its maximum at vertex pointvertex point has t=1.75Therefore, the rock reached its highest point 1.75 seconds after leaving the sling