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**Soroban** Hello, Michael!

(b) The height function is a down-opening parabola.

. . Its maximum value occurs at its __vertex__.

The vertex of a parabola is: x = -b/2a

We have: .a = -0.002, b = 0.4

. . Hence, the vertex is at: .d = (-0.4)(-0.004) = 100

Therefore, the ball reaches maximum height when it is 100 feet from the golfer.

(a) The maximum height is: .h .= .-0.002(100²) + 0.40(100) .= .20 feet

(c) When is height equal to zero?

. . -0.002d² + 0.04d .= .0

Factor: .-0.002d(d - 200) .= .0 . → . d = 0, 200

. . Of course, the ball is on the ground when d = 0.

Therefore, the ball stikes the ground 200 feet from the golfer.