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Viktoria17

  • 2 years ago

Completing the square:

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  1. Viktoria17
    • 2 years ago
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    \[y=-2x-3\]

  2. LogicalApple
    • 2 years ago
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    Is there anything more to this question?

  3. Viktoria17
    • 2 years ago
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    \[y=x ^{2}-2x-3\]

  4. Viktoria17
    • 2 years ago
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    sorry

  5. LogicalApple
    • 2 years ago
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    Ah ok. Sometimes it's easier to work with completing a square by first bringing the constant term to the other side. Start with y + 3 = x^2 - 2x and we can go from there.

  6. Viktoria17
    • 2 years ago
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    y+3?

  7. LogicalApple
    • 2 years ago
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    We added 3 to both sides, so the left side becomes y + 3. This step is not necessary, but it makes completing the square clearer.

  8. LogicalApple
    • 2 years ago
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    You should subtract 2/2 on the right

  9. Viktoria17
    • 2 years ago
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    I dont udnerstand...

  10. LogicalApple
    • 2 years ago
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    We started with this equation: \[y = x^{2} - 2x - 3\] Then, adding 3 to both sides (this is an optional step): \[y + 3 = x^{2} - 2x\] Take the coefficient of the x term, divide it by 2, then square it. That would be (2/2)^2 = 1. So we add 1 to both sides. \[y + 3 + 1 = x^{2} - 2x + 1\] \[y + 4 = x^{2} - 2x + 1\] Notice how the right side factors into a square now: \[y + 4 = (x - 1)^{2}\] Now we can subtract 4 from both sides to get a final solution: \[y = (x - 1)^{2} - 4\]

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