Question

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+26, 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? A. 0.5 in. C. 1.25 in. B. 1 in. D. 2 in.

Answer 1

Answer:

  B.  1 in.

Step-by-step explanation:

For a quadratic of the form ...

  ax^2 +bx +c

The axis of symmetry is found at ...

  x = -b/(2a) = -(-1)/(2·0.01) = 50

The value of the function at x=50 is ...

  h = (0.01·50 -1)·50 +26 = -25+26

  h = 1

The lowest part of the rope is 1 inch above the ground.

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Comment on the solution

It is often easier to evaluate a quadratic or other polynomial if it is written in Horner's form:

  h = (ax +b)x +c

If you evaluate a polynomial using a synthetic division tableau, you will find the sequence of arithmetic operations to be identical.

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A graphing calculator can make short work of a problem such as this.