Question

Use the given information to answer the questions and interpret key features. Use any method of graphing or solving. Round to one decimal place, if necessary.

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) -.25x^2 + 3.42, where x is the number of feet away from the golf club (along the ground) the ball is.

The ball starts ____ feet above the ground.

The ball reaches a maximum height of _____ feet at a horizontal distance of ____ feet away from the golf club 19 it was hit with

The ball returns to the ground at about ____ feet away. ​

Answer 1

The ball starts 3.42 feet above the ground. The ball reaches a maximum height of 3.42 feet at a horizontal distance of 0 feet away from the golf club. The ball returns to the ground at about ±3.7 feet away.

Step-by-step explanation:

The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height of the ball is given by the equation h(x) = -0.25x^2 + 3.42, where x is the number of feet away from the golf club. To find the initial height of the ball, we substitute x=0 into the equation:
h(0) = -0.25(0)^2 + 3.42 = 3.42 feet.

The ball reaches a maximum height at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/(2a). In this case, a = -0.25 and b = 0, so the x-coordinate is x = 0/(2*-0.25) = 0 feet. Substituting this value into the equation, we can find the maximum height:
h(0) = -0.25(0)^2 + 3.42 = 3.42 feet.

The ball returns to the ground when its height is 0. To find the distance from the golf club when this occurs, we set the equation equal to 0 and solve for x:
-0.25x^2 + 3.42 = 0
x^2 = 3.42/0.25
x^2 = 13.68
x = ±√(13.68)
x ≈ ±3.7 feet.