Completing the Square: Changing from General to Transformational Form
Lets start with an easy one…
+2 (There is no coefficient with the “x2” term.)
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Step 1: Move the constant at the end to the other side of the equation. |
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Step 2: Take half the coefficient of the x-term and square it. Add this square to both sides of the equation and simplify |
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Step 3: Factor the right side of the equation into a perfect square. Remember, the constant added to the x in both binomial factors is half the “x” term from step 2 |
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Now lets try a harder one…
(There is a
coefficient with the “x2” term.)
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Step 1: Move the constant at the end to the other side of the equation. |
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Step 2: Factor out the coefficient of the x2-term. |
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Step 3: “Complete the Square.” Take half the coefficient of the x-term and square it. Add this inside the bracket on the right side of the equation. On the left side, add the value multiplied by the value factored out in step 2. |
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Step 4: Factor the right side of the equation into a perfect square |
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Step 5: Multiply both sides of the equation by the reciprocal of the stretch factor. |
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You’re finished!
Breath a sigh of relief… |
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