Question 1180642: 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 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.Create a 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 the answer.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to create a quadratic relation that models a basketball shot hitting the rim from 15 feet away:
**Understanding the Problem:**
* We're given the standard quadratic model for a basketball shot: h = -0.2d² + 3d + 6
* h: height of the ball
* d: distance from the shooter
* We need to create a new quadratic model where:
* The shot is taken from 15 feet away (d = 15).
* The ball hits the rim (we'll assume a standard rim height of 10 feet, so h = 10 when d = 15).
**Creating the New Quadratic Model:**
1. **General Form:** Start with the general form of a quadratic relation: h = ad² + bd + c
2. **Use the Given Information:**
* We know the shot is from 15 feet and hits the 10-foot rim, so we have a point (d, h) = (15, 10). Substitute this into the equation:
10 = a(15)² + b(15) + c
10 = 225a + 15b + c
* To make the shot hit the rim at this distance, we need the vertex of the parabola to be at d = 15. The x-coordinate (in this case, d-coordinate) of the vertex of the parabola is given by -b/2a. So:
15 = -b / 2a
-30a = b
3. **Choose a Value for 'a':**
* We have some freedom here. Let's choose a value for 'a' that's different from the original model but still makes sense for a basketball shot. A slightly smaller value for 'a' would make the shot arc higher. Let's try a = -0.15.
4. **Solve for 'b' and 'c':**
* Using -30a = b and a = -0.15, we get:
b = -30 * (-0.15) = 4.5
* Substitute a = -0.15 and b = 4.5 into the equation 10 = 225a + 15b + c:
10 = 225(-0.15) + 15(4.5) + c
10 = -33.75 + 67.5 + c
c = -23.75
**The New Quadratic Model:**
* h = -0.15d² + 4.5d - 23.75
This model represents a basketball shot taken from 15 feet away that hits the rim of the basketball net.
**Explanation:**
* We used the given information (distance and height of the rim) to create an equation with the general form of a quadratic relation.
* We used the fact that the vertex of the parabola should be at the rim (d = 15) to relate 'a' and 'b'.
* By choosing a value for 'a', we could solve for 'b' and 'c' to complete the model.
Answer by ikleyn(52784)  (Show Source):
You can put this solution on YOUR website! .
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 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.Create a 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 the answer.
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