SOLUTION: The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, y = -0.042x(squared) + 5x, where x is the distance in yards from the point it was hit

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Question 56231This question is from textbook
: The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, y = -0.042x(squared) + 5x, where x is the distance in yards from the point it was hite and y is the height of the golf ball in feet. Assume that the ground is level.
a. Find the maximum height reached by the ball.
b. How far from where it was hit does the ball hit the ground? This question is from textbook

Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, y = -0.042x(squared) + 5x, where x is the distance in yards from the point it was hit and y is the height of the golf ball in feet. Assume that the ground is level.
a. Find the maximum height reached by the ball.
a=-0.42, b=5
max at x=-b/2a=-5/(2(-0.42))=5.95238....
y=14.881 ft.
Comment: It seems highly unlikely that this is the
height. The model is erroneous.

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b. How far from where it was hit does the ball hit the ground?
height = 0 when the ball hits the ground.
0=-0.42x^2+5x
x(-0.42x+5)=0
x=0 or x=11.95 yrds
Comment: Another nonsensicle answer based on the nonsensicle
model you have posted.
Cheers,
Stan H.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The path traveled by a golf ball hit with a 9-iron can be modeled with the quadratic function, y=-0.042x%5E2%2B5x, where x is the distance in yards from the point it was hite and y is the height of the golf ball in feet. Assume that the ground is level.
:
a. Find the maximum height reached by the ball.
The y value of the vertex is the maximum height the ball. We can find the x value of the vertex with the formula:highlight%28x=-b%2F2a%29. The b and a we get from the standard form of a parabola: y=ax%5E2%2Bbx%2Bc. Our a=-0.042 and out b=5.
x=-%285%29%2F%282%28-0.042%29%29=59.5238
Subtstitute that value into y=-0.042x%5E2%2B5x to find the maximum height.
y=-0.042%2859.5238%29%5E2%2B5%2859.5238%29
Plug that into your calculator and you'll find the maximum height to be highlight%28y=148.81ft%29.
:
b. How far from where it was hit does the ball hit the ground?
The x-intercepts represent the position of the ball. Let y=0, factor and solve for x.
0=-0.042x%5E2%2B5x
0=x%28-0.42x%2B5%29
x=0 is the starting position.
-0.42x+5=0
-0.42x=-5
-0.42x/-0.42=-5/-0.42
highlight%28x=199.05ft%29 is where it lands.
Happy Calculating!!!