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Golf Irons Height

Golf Irons Height

The path travelled 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 the ground is level. Find the maximum height reached by the ball and how far from where it was hit does the ball hit the ground? Show all calculations.

y = -0.042x² + 5x

It sure would be helpful to know if pre-calc or calculus soluton is sought.

Assuming pre-calc:
vertex form (completing the square):
y / -0.042 = x² - 5/0.042x
y / -0.042 + (1 / 0.0168)² = x² - 1 / 0.0084x + (1 / 0.0168)²
y / -0.042 + (1 / 0.0168)² = (x - 1 / 0.0168)²
y / -0.042 = (x - 1 / 0.0168)² - (1 / 0.0168)²
y = -0.042(x - 1/0.0168)² + 0.042(1 / 0.0168)²
y = -0.042(x - 1/0.0168)² + 1 / 0.00672

so length of flight is when y = 0 for x > 0:
0 = -0.042x² + 5x
0 = -0.042x + 5
x = 1/0.0084 ≈ 119.05 yds

max height = 1 / 0.00672 ≈ 148.81 yds
distance of max height = 1/0.0168 ≈ 59.52 yds

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