Basketball A player throws a basketball toward the hoop. The basketball follows a parabolic path through the points shown. If the center of the hoop is at (12, 10), will the ball pass through the hoop? (You can think of the units as feet.)
Step 1 Find a quadratic model. Substitute the x and y values into the standard form of a quadratic function. The result is a system of three linear equations.
Use one of the methods from Chapter 3. Solve.
The solution is
Substitute the values into the standard form of a quadratic function. An equation of the parabola is
In terms of the quadratic model, what does it mean for the ball to pass through the hoop?
The point (12, 10) is on the parabola. That is, the point (12, 10) satisfies the quadratic equation.
Step 2 Use the quadratic model to see if the player makes the basket.
The point (12, 10) is on the parabola. The ball will pass through the hoop.
The parabolic path of a thrown ball can be modeled by the table. The top of a wall is at (5, 6). Will the ball go over the wall? If not, will it hit the wall on the way up, or the way down?
x | y |
---|---|
1 | 3 |
2 | 5 |
3 | 6 |