A soccer player kicks a ball downfield. The height of the ball increases until it reaches a maximum height of 8 yards, 20 yards away from the player. A second kick is modeled by y=x(0,4 – 0.008x). Which kick travels farther before hitting the ground? Which kick travels higher?

Step-by-step explanation:

Assuming the kick started from ground level, the path of the ball is assumed to be symmetrical about the high point. That is, the first kick will land 2×20 = 40 yards downfield.

The equation for the second kick can be rewritten as ...

  y = 0.008x(50 -x)

The value of y will be zero at x=0 and at x=50. The second kick will land 50 yards downfield, a greater distance than the first kick.

At x=25, the height of the second kick is ...

  y = 0.008(25)(50-25) = 5 . . .  yards

The second kick travels farther (50 yds vs. 40 yds).

The first kick travels higher (8 yds vs. 5 yds).

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