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In lesson 5 of Teaching Company's Algebra II course, what is being said does not match the graphics. This is new material for me, so I just wondered if anyone else has encountered this, or if I'm just not understanding somehow.

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Okay, after a little research I'm pretty sure there is a mistake. His rule states that for a parabola(He doesn't call it that, but that's what it is) the equation y=(x-a)squared, if a is positive it will make the parabola move to the right and if a is negative it will move to the left. Find just the opposite to be true. Also, the graphics show differently from this.

I hope that makes sense to someone. Help!

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Okay, after a little research I'm pretty sure there is a mistake. His rule states that for a parabola(He doesn't call it that, but that's what it is) the equation y=(x-a)squared, if a is positive it will make the parabola move to the right and if a is negative it will move to the left. Find just the opposite to be true. Also, the graphics show differently from this.

I hope that makes sense to someone. Help!

We all agree that y = x^2 is a parabola based at the origin which opens up.

Now, if we consider y = (x - 3)^2, we have the same parabola from above translated (i.e. shifted) three units to the right.

y = (x + 3)^2 is the generic parabola with a shift of three units left.

In terms of "a" from your comment, in my first translated example, a = 3. The shift was to the right.

In the next example, we rewrite y = (x + 3)^2 = (x - (-3))^2 to see that a = -3. The shift is the left.

I believe the author is correct.

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Okay, Jane, bear with me as I'm new to this. Let me make sure I understand you. You're saying that because the formula is x-a that when a is positive it would appear as x-(a) which would make it appear negative as in x-a when you multiply the negative sign through? And if I had x- (-a) then it would appear positive for the same reason? So, y=(x+3) squared looks like y=(x-(-3)) squared and then I multiply the negative sign throug to get y=(x-3) squared?

Do you think I'm understanding you? It's hard to write out, but I think I get it. He did not make this clear at all on the video.

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Okay, Jane, bear with me as I'm new to this. Let me make sure I understand you. You're saying that because the formula is x-a that when a is positive it would appear as x-(a) which would make it appear negative as in x-a when you multiply the negative sign through? And if I had x- (-a) then it would appear positive for the same reason? So, y=(x+3) squared looks like y=(x-(3)) squared and then I multiply the negative sign throug to get y=(x-3) squared?

Do you think I'm understanding you? It's hard to write out, but I think I get it. He did not make this clear at all on the video.

Yes, I think you've got it.

If the formula were x + b, then when we would write x + 4, b = 4.

But the formula is x - a. Think of it as x - [ ]. (I want to draw a box on the white board and call this x minus box.) If what you place in the box is a negative number, then when you distribute the minus from outside of the box, you get a quantity with a "+".

I hope that I am being clear. Maybe?

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Okay, I see it now. But, he did not make this clear at all. The formula was embedded in the text of the rule and he never mentioned it. I am loving this series so far, but everything else has been review.

Thanks for your help, I may be asking more questions. I'm glad I chose to watch these with my dd, so I can help clear up any fuzzy areas.

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Happy to help.

If you post questions on this board, one of the math people will usually chime in pretty quickly.

Glad to hear good things in general about the TC Algebra II course.

Jane