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anonymous

  • 5 years ago

how do you complete the square

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  1. anonymous
    • 5 years ago
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    depends on the context. are you trying to solve a quadratic equation?

  2. anonymous
    • 5 years ago
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    no parabolas

  3. anonymous
    • 5 years ago
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    they are the same thing

  4. anonymous
    • 5 years ago
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    ah then you want to find the vertex by comleting the square. i.e. you want to write \[y=ax^2+bx+c\] as \[y=a(x-h)^2+k\] right

  5. anonymous
    • 5 years ago
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    \[x^2 +bx+c=x^2+bx+(b/2)^2-(b/2)^2+c=(x+b/2)^2+c-(b/2)^2\]

  6. anonymous
    • 5 years ago
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    here is an easy method with an example. the vertex is always where \[x=-\frac{b}{2a}\] so if i see \[y=x^2-6x+5\] i know the first coordinate of the vertex will be \[-\frac{6}{2(-1)}=3\] and the second coordinate will be what i get when i replace x by 3 namely -4 so i know it is \[y=x^2-6x+5=(x-3)^2-4\]

  7. anonymous
    • 5 years ago
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    here is another method. if you have \[y=ax^2+bx+c\] you can rewrite as \[y=a(x^2+\frac{b}{a}x)+c\] and then write \[y=a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a}\] but that seems unnecessarily complicated

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