What is the function that represents the height of the ball in terms of it’s distance from a player

Question

7. A football player kicks a football across the football field. The ball leaves the player's foot at a height of 2 ft. It follows a path in the shape of a parabola.

At the highest point, the ball is a horizontal distance of 15 feet from the player and 8 feet above ground. What is the function that represents the height of the ball in terms of its distance from a player?

Answer 1

Do you mean actual distance to the ball (very difficult) or just horizontal distance (x coordinate). If it's just x coordinate, you are finding the parabola that fits the data:

It will be a vertically shifted (by 2) parabola of the form k(x)(x-30) = y from the zeroes. Find k from the max height at the midpoint (15, 6) (note that the max height is adjusted for the symmetrical parabola 2 feet lower at every point:

6 = k(x)(x -30) k = -6/225

The final equation would be (-6/225)(x)(x-30) + 2 = y

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