Question

The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x)=−.15x2+3.2x, where x is the number of feet away from the golf club (along the ground) the ball is.
The ball reaches a maximum height of _______ feet at a horizontal distance of ____
feet away from the golf club it was hit with.
The ball returns to the ground at about ________ feet away.

Answer 1

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Answer:

  maximum height of 17.07 feet about 10.67 feet from the club

  returns to the ground 21.33 feet away

Step-by-step explanation:

A graphing calculator can answer these questions easily.

The vertex of the quadratic ax²+bx+c is given by x=-b/(2a). For this quadratic function, the highest point is found at ...

  x = -(3.2)/(2(-0.15)) = 32/3 = 10 2/3 . . . . feet horizontally from the club

The maximum height is the function value at that point.

  h(10 2/3) = (-0.15(10 2/3) +3.2)(10 2/3) = 1.6(10 2/3) = 17 1/15

The ball reaches a maximum height of 17 1/15 feet at a horizontal distance of 10 2/3 feet from the club. The ball's flight is symmetrical about the peak, so it returns to the ground about 21 1/3 feet away.