A person 6 ft tall wants to buy a jump rope. If, when the rope is at its lowest point, their hands will be 3 ft apart and 3 ft above the ground and if the rope will take on the shape of a parabola just barely hitting the ground, how long must the rope be?
Consider the rope to be described by the equation y=ax^2 with the origin being a spot on the ground where the jump rope touches.
arc length = sqrt(1+(dy/dx)^2)

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wouldnt that be a caternary and not a parabola?

we can find the "parabola" by wrapping our curve around the 3 points established

(0,0) (-1.5,3) (1.5,3)

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