UCSS Math II 5.9.5 Example 4

The potential energy in joules of an oscillating spring can be represented by the expression , where is a constant and is the time in seconds since the spring began oscillating. Create a two-column proof to show that the potential energy of the spring can also be written as .
  1. Create the outline for the two-column proof.
  2. Rewrite the fraction on the left side of the equation as the difference of two fractions.
  3. Simplify .
  4. Use the reciprocal identity to rewrite the expression from step 3.
  5. Use the Pythagorean identity to rewrite the expression .
  6. Fill in the columns of the two-column proof.
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