Question 1195721: 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?
e. Create a graphical model, using technology, to verify your calculations.
f. Create your own quadratic relation that would model the path of a shot from a distance of
15 feet that would hit the rim of the basketball net. Explain how you obtained your answer
I genuinely have no clue where to start on this, so even just a little help would be greatly appreciated :)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! h=-0.2d^2+3d+6. The constant 6 is the height the ball started from when d=0. So that is a.
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b. maximum height is the vertex and that is when d=-b/2a, where b=3 and a=-0.2
so that is when d=-3/-0.4 or 7.5
now substitute that to get 17.25 feet
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c. Want to know what d was when h=10
10=-0.2d^2+3d+6
0=-0.2d^2+3d-20
Make this d^2-15d+20=0 multiplying by -5 both sides
quadratic formula d=(1/2)(15+/- sqrt (145)=1/2 (15 +/-12.04)
d=13.52 feet from shooter and 1.48 feet, for a distance of 12.04 feet.
graph this
Mathematically, it hits the rim and 1.48 feet away and at 13.52 feet away. Realistically, the first would be hitting on the way up, which isn't going to work, but 13.52 feet would work.
See if this helps.
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