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  1. MHB Apprentice

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    #1
    What is the x-intercept of the graph of y = x2 4x + 4?

    How would you foil this?

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    #2
    To find the x intercept of the graph of the function $y = x^2 4x + 4$

    We may either use the completing the square method or we may use the formula $x=\frac{-b}{2a}$

    The easiest way is to use $x=\frac{-b}{2a}$

    From $y = x^2 4x + 4$ which is in the form of $ax^2+bx+c$ we can find the values for $b$ and $a$ as $b=-4$ & $a=1$

    $-b$ in the formula stands for the opposite of the value of $b$ in the above form.

    $x=\frac{-(-4)}{2*1}$
    $x=\frac{4}{2}$
    $x=2$

    using complete the square method to form the graph of the function of the form $y=\pm(x+b)^2+c$ or the vertex form

    $y= (x^2 4x+(\frac{b}{2})^2 ) + 4 - (\frac{b}{2})^2 ) $
    $ y=(x^2 4x+(\frac{-4}{2})^2 ) + 4 - (\frac{-4}{2})^2 ) $
    $ y=(x^2 4x+4 ) + 4 - 4 $
    $y=(x-2)^2$

    which now the x means -b which is 2.

    Now it can be seen using Desmos one $x$ intercept of both the forms is $(2,0)$

    Last edited by mathlearn; December 19th, 2016 at 04:59.

  3. Pessimist Singularitarian
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    #3
    Quote Originally Posted by 816318 View Post
    What is the x-intercept of the graph of y = x2 4x + 4?

    How would you foil this?
    To find the $x$-intercept, we can set $y=0$ and solve for $x$:

    $ \displaystyle x^2-4x+4=0$

    To factor, we need to look for two factors of 4 whose sum is -4, and we find:

    $ \displaystyle (-2)(-2)=4$

    $ \displaystyle (-2)+(-2)=-4$

    Thus, the factored form is:

    $ \displaystyle (x-2)(x-2)=0$

    or:

    $ \displaystyle (x-2)^2=0$

    We have a repeated root, of multiplicity 2. Since the multiplicity is even, we know the graph will touch the $x$-axis without passing through it. Equating this factor to zero, we find:

    $ \displaystyle x-2=0$

    $ \displaystyle x=2$

    Thus, we know the given graph has one $x$-intercept at $(2,0)$.

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    #4
    $$x^2-4x+4=x^2-2x-2x+4=x(x-2)-2(x-2)=(x-2)(x-2)=0\implies x=2$$

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