Lesson Summary

During this chapter, the project at hand involves creating a simulation to depict the trajectory of a basketball being thrown into the air towards a basket. The simulation will showcase how a basketball player throws the ball towards the basket, aiming to precisely describe the trajectory.

The challenge is to develop a function that correlates the distance on the horizontal axis with the height of the ball at different points during its trajectory towards the basket. A linear relation is not suitable for this task as it would result in an unrealistic motion, unlike the curved trajectory of a basketball in real life.

The curved trajectory of the basketball is due to the initial impulse being divided into forward and upward directions. This combination of motions results in the curved path. Gravity also plays a crucial role, pulling the ball towards the earth's center, leading it to reach a maximum height before descending back to the floor.

The ultimate aim is for the trajectory of the ball to intersect with the basket, ideally resulting in a successful shot. To achieve this, various relations and functions need to be explored to model the curved trajectory accurately.

The first task involves creating a table with different values for the independent variable (x) ranging from -3 to 3. The equation y = x² will be used to calculate the corresponding y values for each x. The points from this table will be plotted on a coordinate system to visually represent the trajectory, which should form a smooth curve.

Finally, after completing the table and plotting the points, you are encouraged to analyze the graphic created, detailing its features and characteristics in the comments section, which will be further discussed in upcoming lessons.