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use completing the square to describe the graph of each function.

How do you complete the square with this equations. please show me step by step so that I can understand it.


  • Precalc -

    x^2 - 4x + 6
    first, yo only focus on the first two terms: x^2 and -4x. let's put a parenthesis to enclose them:
    (x^2 - 4x) + 6
    now, to complete the square, what we do is get the half of b (b is the numerical coefficient of x, and in this case, is -4) and we square it: (-4/2)^2 = 4. Then we add a term +4 inside the parenthesis, but to remain the value of the whole expression constant, we also put a -4 but outside the parenthesis:
    (x^2 - 4x + 4) + 6 - 4
    the term inside the parenthesis is a perfect square, and we can further simplify this into:
    (x-2)^2 + 2

    hope this helps~ :)

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