Personal Project - The Wizard of Oz.ppt
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Transcript of Personal Project - The Wizard of Oz.ppt
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This presentation is automatic and contains audio and
interactive directions. Please be sure your sound is turned on
and that you await all transitions and follow all
instructions. Thank you.
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You are about to travel to a
mystical land…
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That many have heard of,
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That many have heard of,
but few have ever seen.
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Welcome to
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OZThe
Land of
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End Behaviors
of a function
Define a polynomi
al function
Factored form of polynomial
from x-intercepts
Identify zeros of a function
Determine number of real and non-real
solutions
Long division of
polynomialsSynthetic division to find zeros
Click a bubble to explore….
Polynomial Functions in…
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Welcome to Munckinland Dorothy. Would you like to
learn about the end behaviors of functions?
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The first thing that you need to know is that the
degree of a function determines which direction the end behaviors go. The Lollipop Guild will
explain.
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So Dorothy. There are two different ways end behaviors can react in a polynomial
function. It can either look like a rainbow, like the beautiful ones we have in Oz, or like a funny sideways “s” thing. Ya’ understand?
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I think so. You wouldn’t by chance have any pictures
would you?
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Eh. Pictures. The gal wants pictures. Don’t worry, we got
some right here.
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Lookie here. If we had an equation that had an even number as a degree, it’d look like this thing here. As you can tell, the end
behaviors are:X → - ∞ Y→∞
andX → ∞ Y→ ∞
But if the equation were reflected over the x- axis and the arch went the other way, both Y end behaviors would be -∞
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And this is the funny “s” thing that equations with an odd degree look like when they’re graphed. Kind of weird, huh?
This equation’s end behaviors are: X→-∞ Y→-∞X→∞ Y→∞
If it were reflected over the x-axis, they would be:X→-∞ Y→∞X→∞ Y→-∞
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Do you understand darling?
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Yes. I think I do. Thank you Glinda.
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End Behaviors
of a function
Define a polynomi
al function
Factored form of polynomial
from x-intercepts
Identify zeros of a function
Determine number of real and non-real
solutions
Long division of
polynomialsSynthetic division to find zeros
Click a bubble to explore….
Polynomial Functions in…
![Page 21: Personal Project - The Wizard of Oz.ppt](https://reader037.fdocuments.net/reader037/viewer/2022110323/55cf8fdb550346703ba08e26/html5/thumbnails/21.jpg)
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Scarecrow? Are you there?
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Over here Dorothy.
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Oh there you are! I have a question, do you know
anything about using long division with polynomial
functions?
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Do I know anything? Haven’t you heard? I have a brain now!
Of course I know how to use long division with polynomial
functions. Watch this:
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Pay attention to the leading x of the divisor and x² of the dividend. If you were to divide x² by x, what
would you have? X. Put that on top.
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There. Now multiply that x that you just put on top by x+1, which turns into x² + 1x. Put that under
the x² and 9x of the dividend.
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Perfect! You can now subtract x² +1x from x²-9x.
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Fantastic. Now you can carry the -10 down from the dividend.
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Now the process starts all over again. Take the -10x and divide it by the x of the divisor. It turns
into -10, so put that on top.
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So now what you want to do is take the -10 that you just put on top and multiply it by the x+1. It turns into -10x-10. Put that under the other -10x-
10. Now subtract just like you did before.
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And presto! Your work is done.
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Oh Scarecrow, thank you! That makes it so
much clearer.
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No problem Dorothy, I’d do anything to help. You are the one who helped
me get this brain. But now you better be off. You have many other things
to learn…
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End Behaviors
of a function
Define a polynomi
al function
Factored form of polynomial
from x-intercepts
Identify zeros of a function
Determine number of real and non-real
solutions
Long division of
polynomialsSynthetic division to find zeros
Click a bubble to explore….
Polynomial Functions in…
![Page 37: Personal Project - The Wizard of Oz.ppt](https://reader037.fdocuments.net/reader037/viewer/2022110323/55cf8fdb550346703ba08e26/html5/thumbnails/37.jpg)
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Tin man? Tin man? I’ve heard you can teach me
synthetic division.
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Synthetic division? I can help you with that. It’s quite easy.
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Let’s look at the equation x²+5x+6 and try to divide it by x-1. First take all of the coefficients
and draw them inside a boxed section.
x² + 5x+6
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. Just like that.
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Now take the 1 form x-1 and plant it outside of the box.
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Take the first coefficient and slide it down the division symbol.
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Then multiply the one you just carried down by the planted one, and put the product under the next
coefficient, which would be 5.
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Add 5 and 1 to get 6, and place that under the division bar.
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Excellent! Now the process repeats itself. Multiply the carry down by one and place it under the next
coefficient.
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Finally, add 6 and 6. The answer, if other than 0, is the remainder. 12 is the remainder here.
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I had no idea it was that simple. That was incredibly helpful, thank you.
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Why, you’re welcome! Have fun on your other adventures!