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iHOOP96
im currently studying transformations in my math class, and i am totally confused. Can someone please specify the basics ?
what kind of transformation?
(algebra 1) with reflections, and quadratic, linear,etc
I've got you covered. It depends on what kind of equation you are transforming. Line? Circle? Ellipse? Parabola? Hyperbola?
y=-(x+1)-2 and behind the last parenthesis is suppost to be to the 3rd power
That's a Line. so, the slope is made negative by the minus 1 before the parentheses. The term in the parentheses is x-1, so you have x - - 1 to give you x+1 there so you shift to the left by 1. That's the key. Remember that term is always x-d, so if you see a plus remember it's really --d. The -2 shifts horizontally downward by 2.
thank you. and i have more questions, do you mind answering them?
Oh, wait a minute. I didn't see your cube. are you sure that's not a second power?
A SECOND POWER on that term makes it a parabola.
And where I said slope is negative, what you have then is a parabola opening downward.
ok , heres the next one..
And the thing that minus 1 before the parantheses does is reflect it across the x axis to make it point downward. Do you see that?
yes it just confused me because i dont understand how should i know when to flip it over the y-axis or x-axis.
Where you see the X reflection is the term outside the parentheses. Where you see the Y reflection is the sign of the first guy in the parentheses. f(x) = a(x-h)^2 +k + or minus on the a term is reflection across the x-axis. + or - on the x term is reflection across the y-axis. the sign of h is the shift left (-) to right (+), IMPORTANTLY remember the minus in x-h is always there regardless of what the sign hidden in h is. (x+h) is really [x-(-h)]. (x-h) is really [x-(+h)]. and the sign on the k term drives the vertical shift (+ is up, - is down).
If you have a graphing calculator, or can download Microsoft Math (free), or can go to the wolfram site, you should experiment with entering an equation and changing each value to see what happens. That's how I learned it. You can test your thinking that way, too.