Question

Instructions: 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)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.

1) The ball starts (blank/answer) feet above the ground.

2)The ball reaches a maximum height of (Blank/answer) feet at a horizontal distance of (blank/answer) feet away from the golf club it was hit with.

3)The ball returns to the ground at about (blank/answer) feet away.

Answer 1

1.) Zero ( 0 )

2.) 55.47 feet , 8.6 feet

3.) 17.2 feet

Explanation:

The height, in feet, of the ball is given by the equation h(x)=−.25x2+4.3x, where x is the number of feet away from the golf club (along the ground) the ball is.

1.) Since the equation has no intercept,

The ball will start zero feet above the ground.

2.) The distance of the ball at the maximum height will be achieved by using the formula

X = -b/2a

Where b = 4.3, a = -0.25

Substitutes both into the formula

X = -4.3 / 2( - 0.25 )

X = - 4.3 / - 0.5

X = 8.6 feet

Substitute X into the function to get the maximum height

h(x) = −.25(8.6)^2 + 4.3(8.6)

h(x) = 18.49 + 36.98

h(x) = 55.47 feet

3) As the ball returns to the ground, the height will be equal to zero, therefore,

0 = -0.25x^2 + 4.3x

0.25x^2 = 4.3x

X = 4.3/0.25

X = 17.2 feet

The ball returns to the ground at about 17.2 feet away