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Math Help - Matrix Transformations

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    Matrix Transformations

    With transformations of [3,2] and [2,-2], i am to find the image of the following equations(noting that each of the above transformations are treated separately for each equation:

    a)y=|x|
    b)y=x^2-3x
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    Quote Originally Posted by johnsy123 View Post
    With transformations of [3,2] and [2,-2], i am to find the image of the following equations(noting that each of the above transformations are treated separately for each equation:

    a)y=|x|
    b)y=x^2-3x
    First get the transformation matrix. Can you do this? Please show what you've tried and say where you get stuck.
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    i am critically most stuck on applying the transformations(they're are horizontal and vertical) of [3,2] and [2,-2] to the equation x^2-3x.
    i factorized x^2-3x which came out to be x(x-3) and then i applied the transformations seperately, which is what is asked, but then it got a lil messy and wrong.
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    Quote Originally Posted by johnsy123 View Post
    With transformations of [3,2] and [2,-2], i am to find the image of the following equations(noting that each of the above transformations are treated separately for each equation:

    a)y=|x|
    b)y=x^2-3x
    Here's how to do part b) i), you follow the same procedure to do part b) ii)...

    If you remember back to when you studied quadratics, the quadratic equation \displaystyle y = a(x - h) + k represents a translation of \displaystyle (h, k) to the equation \displaystyle y = ax^2.

    So for your quadratic \displaystyle y = x^2 - 3x

    \displaystyle = x^2 - 3x + \left(-\frac{3}{2}\right)^2 - \left(-\frac{3}{2}\right)^2

    \displaystyle = \left(x - \frac{3}{2}\right)^2 - \frac{9}{4},

    applying the transformation \displaystyle (3, 2) gives

    \displaystyle y = \left(x - \frac{3}{2} - 3\right)^2 - \frac{9}{4} + 2

    \displaystyle = \left(x - \frac{9}{2}\right)^2 - \frac{1}{4}

    \displaystyle = x^2 - 9x + \frac{81}{4} - \frac{1}{4}

    \displaystyle = x^2 - 9x + 20.
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