A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h=0.01x^2 - x + 28, where h is the height (in inches) above the ground and x is the distance (in inches) along the ground measured from the horizontal position of one end. How close to the ground is the lowest part of the rope?

Question

Kieran Larson

Mathematics

30 June, 13:20

A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h=0.01x^2 - x + 28, where h is the height (in inches) above the ground and x is the distance (in inches) along the ground measured from the horizontal position of one end. How close to the ground is the lowest part of the rope?

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Answers (1)

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Jonathan · Answer 1

The lowest height of a parabola ax²+bx+c is when x=-b/2a

in this case, b=-1, a=0.01, so x=1/0.02=50

when x=50, h=0.01*50²-50+28=3

so the lowest part of the rope is 3 feet inches above the ground.