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?

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).

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?​

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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?