WEBVTT
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This is part 9 of parabolas and we're going to graph this function f of x equals negative
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to x squared plus 6x as well as state all of the things I have here on the left.
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All right, so let's go ahead and get started.
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So the axis of symmetry, well notice this is in the form a x squared plus b x plus c of course c is zero
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in this case. So it's easy to use the formula x equals negative b over 2a to get the axis of symmetry.
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So I'm going to have negative, my b value is 6 over 2 times negative 2.
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All right, so that's going to end up being positive, right?
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Because I have another negative, so 6 force is going to be 3 halves.
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So my vertex, I'm sorry, my axis of symmetry is x equals 3 halves, which means my vertex point is going
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to have 3 halves for the x coordinate.
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All right, so now we know that the x coordinates 3 halves, how am I going to get the y coordinate?
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I have to go back up to the function and plug in 3 halves.
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So if the function is f of x equals negative 2 x squared plus 6 x, I have to plug in 3 halves for x.
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All right, so I'm putting in 3 halves squared plus 6 times 3 halves.
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Now you can't get rid of those fractions by the way, you're just simplifying.
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Don't try multiplying both sides by the least common denominator.
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There aren't really two sides, you're just simplifying.
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So this is negative 2 times, well 3 halves times 3 halves is 9 force plus.
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And I'm going to go ahead and leave this as 18 halves.
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Because I'm going to get a common denominator in a minute.
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You could have, you know, canceled and say that that was 9.
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But notice that I can cancel this and I have a negative 9 halves plus 18 halves.
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So negative 9 halves plus 18 halves is 9 halves.
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So my y value for my vertex point is 9 halves.
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So it's going to be 3 halves, 9 halves.
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Now if you want, you could write that as 1 and a half, 4 and a half, right?
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Same thing.
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So let's go back up here.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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And I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.
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So I'm going to go ahead and leave this as 18 halves.