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Put the equation y=x²+6x+5 into the form y=(x-h)²+k :

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Final answer:

The equation y = x² + 6x + 5 can be rewritten in the form y = (x - h)² + k by completing the square, resulting in y = (x + 3)² - 4.

Step-by-step explanation:

To put the equation y = x² + 6x + 5 into the form y = (x - h)² + k, we need to complete the square


  1. First, we rewrite the quadratic term and the linear term: y = x² + 6x.

  2. To complete the square, take half of the coefficient of x, which is 3, and square it, getting 9. Then add and subtract this number inside the parentheses: x² + 6x + 9 - 9.

  3. Rewrite the equation with a perfect square trinomial: y = (x + 3)² - 9 + 5.

  4. Combine the constant terms to get the final form: y = (x + 3)² - 4.


The equation in the form y = (x - h)² + k is now y = (x + 3)² - 4.

User Arthur Tacca
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