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
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- First, we rewrite the quadratic term and the linear term: y = x² + 6x.
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- 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.
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- Rewrite the equation with a perfect square trinomial: y = (x + 3)² - 9 + 5.
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- 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.