SOLUTION: 1. A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the

Question 1180599: 1. A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h = - 0.2d2 + 3d + 6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet.

a. How high was the ball when the shooter shot it?
b. What was the maximum height obtained by the ball?
c. A rim of a basketball net is 10 feet high. For what distance was the ball above the rim of the basketball net?
d. How far would the shooter have to be away from the rim of the basketball net for the ball to hit the rim of the basketball net and possibly go in?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
6 feet, the constant in the quadratic.
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The maximum height occurs at d=-b/2a or -3/-0.4 or 7.5
h(7.5)=17.25 feet.
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set h(d)=10
so -0.2d^2+3d+6=10
and 0.2d^2-3d+4=0
d^2-15d+20=0, multiplying by 5
d=(1/2)(15+/- sqrt(225-80)); sqrt 145=12.04
the distance will be 1.48 feet and 13.52 feet
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There are several possible solutions since the ball doesn't have to be dead center to go in, but since there isn't information about that, we can still figure the optimum distance. That would be when the quadratic equals 10 above, so the distance would be 13.52 feet. The other solution would require the ball to be traveling upward through the net and that would not be allowable.
Remember that the 17 foot distance where the ball lands on the floor would only be if it didn't go through the net.

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