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Convert From General to Standard Form

  1. Nov 16, 2009 #1
    Hey everyone, I was wondering if you could help me with something.

    Can someone give me the step to convert the two equations from general to standard form? If you could, it would be such a great help to me. Thanks

    y= x^2 - 2X + 5 and y= -3x^2 + 12x -4
     
  2. jcsd
  3. Nov 16, 2009 #2

    Mark44

    Staff: Mentor

    It's been quite a few years, so I don't recall what standard form looks like. Is it like this?
    y = A(x - h)2 + k

    If so, what you need to do is complete the square in your x terms. For example, if your equation was y = -2x2 - 4x + 7, you would do this.

    y = -2x2 - 4x + 7

    Factor -2 from each of the x terms, getting this:
    y = -2(x2 + 2x) + 7

    Complete the square inside the parentheses, keeping track of what you really added.
    y = -2(x2 + 2x + 1) + 7 + 2

    In the step above, it looks like I added 1, but I really added -2, so to keep the right side equal to what it was, I have to balance that by adding + 2.

    y = -2(x + 1)2 + 9

    Not sure if this is the form you're looking for, but it is very useful nevertheless. Here we have the equation of a parabola whose vertex is located at (-1, 9).

    If this is the form you're looking for, apply the same technique to your problems.
     
  4. Nov 16, 2009 #3
    thanks!
    can anyone help me with the second one?
     
  5. Nov 16, 2009 #4

    symbolipoint

    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    The second one would be easier if you factor into -3 and the appropriate quadratic polynomial.

    y= -3x^2 + 12x -4 = -3(x^2 - (-4)x + (4/3))

    Now you want to focus most of your attention to completing the square for the polynomial, and then clean the remaining steps.
     
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