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Math Help - x2 + 4x + 5

  1. #1
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    x2 + 4x + 5

    How would I write this quadratic (x2 + 4x + 5) in standard, factored, and vertex forms?

    Thanks.
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  2. #2
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    Quote Originally Posted by Andrew00830 View Post
    How would I write this quadratic (x2 + 4x + 5) in standard, factored, and vertex forms?

    Thanks.
    x^2 + 4x + 5 is already in standard form.

    To get vertex form, complete the square: (x + 2)^2 - 4 + 5 = (x + 2)^2 + 1.

    It should be obvious from the vertex form that it cannot be expressed in factorised form using real linear factors.
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  3. #3
    Senior Member pacman's Avatar
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    x^2 + 4x + 5= 0, complete the square,

    x^2 + 4x + (4/2)^2 = (4/2)^2 - 5

    (x + 2)^2 = 4 - 5 = -1

    (x + 2) = (+/-) sqrt (-1); where sqrt (-1) = i

    x + 2 = (+/-)i

    you have 2 roots: x = -2 + i and x = -2 - i

    VERTEX FORM? - that is not clear to me because your equation is in the root finding form. If it for graphing purposes, should it be written in this form (x - h)^2 = 4a(y - k) or what? thanks for clarifying . . . . i may mis-interpret what you mean.

    may it be in the form: y = x^2 + 4x + 5?

    then x^2 + 4x + 4 = y - 5 + 4, the number 4 was added BS to complete the square.

    (x + 2)^2 = y - 1

    vertex: (h,k) = (-2,1). see graph attached
    Attached Thumbnails Attached Thumbnails x2 + 4x + 5-awe.gif  
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