# Matrix Transformations

• Feb 18th 2011, 05:44 PM
johnsy123
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
• Feb 18th 2011, 05:48 PM
mr fantastic
Quote:

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.
• Feb 18th 2011, 06:16 PM
johnsy123
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.
• Feb 18th 2011, 06:20 PM
Prove It
Quote:

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 $\displaystyle \displaystyle y = a(x - h) + k$ represents a translation of $\displaystyle \displaystyle (h, k)$ to the equation $\displaystyle \displaystyle y = ax^2$.

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

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

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

applying the transformation $\displaystyle \displaystyle (3, 2)$ gives

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

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

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

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