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Math Help - Quadratic function

  1. #1
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    Quadratic function

    determine the maximum or minimum value of each of the following quadratic functions by completing the square. state the value of X corresponding with the maximum or minimum value

    1. f(x)= x(square) - 6x + 2

    2. f(x)= 3x(square) + 9x + 7

    3. f(x)= 1 - 4x - x(square)


    answer with solution plz.. "x(square) is x2" the digit 2 is too big
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  2. #2
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    Quote Originally Posted by callisto200 View Post
    determine the maximum or minimum value of each of the following quadratic functions by completing the square. state the value of X corresponding with the maximum or minimum value

    1. f(x)= x(square) - 6x + 2

    2. f(x)= 3x(square) + 9x + 7

    3. f(x)= 1 - 4x - x(square)


    answer with solution plz.. "x(square) is x2" the digit 2 is too big
    I'll do the first question to show you what you should do. Please publish your work so we have a chance to help you more specifically:

    f(x)=x^2-6x+2

    Consider x^2-6x as the beginning of a complete square where the final square number is missing. If you have ax^2 +bx then the final square is \left(\dfrac b{2a}\right)^2 . In your case a = 1. Thus the final number is \left(\dfrac6{2}\right)^2 = 9.

    If you add 9 to get a complete square you must subtract the 9 at once so that the equation is still true:

    f(x)=x^2-6x\bold{\color{red}+9}\bold{\color{red}-9}+2

    Now collect the first 3 summands:

    f(x)=(x-3)^2-7

    The equation belongs to a parabola opening up. Thus the vertex is the minimum point. At x = 3 the function has ist smallest value f(3) = -7

    And now it's your turn!
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