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Math Help - Quadratics

  1. #1
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    Quadratics

    how do i find the minimum value or maximum value of function
    x^2-12x+9?
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  2. #2
    Super Member
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    Quote Originally Posted by Rose Wanjohi View Post
    how do i find the minimum value or maximum value of function
    x^2-12x+9?
    Rewrite it in vertex form:
    y = a(x - h)^2 + k.

    If the leading coefficient is positive, then the vertex (h, k) is the minimum point; if the leading coefficient is negative, then the vertex (h, k) is the maximum point.

    So, we complete the square to rewrite the equation in vertex form:
    x^2-12x+9
    \begin{aligned}<br />
&= x^2 - 12x \;{\color{red}+\;36}\;+ 9\; {\color{red}-\;36} \\<br />
&= (x - 6)^2 - 27<br />
\end{aligned}

    The leading coefficient was positive (a = 1), so the point (6, -27) is the minimum of the parabola.


    01
    Last edited by mr fantastic; July 18th 2009 at 03:59 AM.
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by Rose Wanjohi View Post
    how do i find the minimum value or maximum value of function
    x^2-12x+9?
    Hello: The formula for the minimum or the
    the maximum point by the function f(x) = a x 2 +bx +c is :
    (-b/2a; f(-b/2a))
    In this exercice : a =1 , b= -12 c =9
    I'have : (-(-12)/2 ,f(6))
    f(6) = 36-12(6)+9=-27 Conclusion : A ( 6 , -27 )
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