Matrix Transformations

**johnsy123** · February 18th 2011, 05:44 PM

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

**mr fantastic** · February 18th 2011, 05:48 PM

Originally Posted by johnsy123

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.

**johnsy123** · February 18th 2011, 06:16 PM

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.

**Prove It** · February 18th 2011, 06:20 PM

Originally Posted by johnsy123

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

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

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

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

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

Thread: Matrix Transformations

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