WEBVTT
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Let's find the ember seven function. So we start
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by switching X and y, so that would give
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us X equals Y squared minus y. Now we
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went to isolate Why? So this is a little
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tricky because it's very difficult to isolate. Why in
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a quadratic function, unless you change it to a
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different form. So what I'm going to do is
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complete the square. And to do that, I'm
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going to figure out what I need to add to
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make a perfect try. No meal square. So
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we've y squared minus one. Why? Plus now
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, to get the number that we add, we
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take half of the coefficient on Why? So that
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would be negative. 1/2 and we square it,
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and that would be 1/4. So we need to
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add 1/4. Now. We can't just add 1/4
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to 1 side of the equation. We have to
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add it to both sides of the equation. So
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let's add it to the other side as well.
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So we have X plus 1/4. All right.
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Now we can rewrite our perfect try. No meal
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square in its factored form. Why minus 1/2 quantity
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squared. Okay, remember, our goal is to
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isolate why. So let's go ahead and square root
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both sides of the equation now and we get the
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square root of X plus 1/4 equals Why minus 1/2
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. And finally, we're going to add 1/2 to
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both sides. So we have the square root of
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X plus 1/4 plus 1/2 equals Why? And instead
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of calling it why we want to call it f
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of X or f inverse of X. Well,
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actually, in this case, we don't have to
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, because the original function was not called F of
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X. So I suppose we don't have to call
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this f in verse, but if we want to
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, I think the answer key has FM for so
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I'll go along with that and there we have it
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.