how do you complete the square

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how do you complete the square

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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depends on the context. are you trying to solve a quadratic equation?
no parabolas
they are the same thing

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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
\[x^2 +bx+c=x^2+bx+(b/2)^2-(b/2)^2+c=(x+b/2)^2+c-(b/2)^2\]
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 \[y=x^2-6x+5=(x-3)^2-4\]
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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