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In this video we're going to look at how to use the calculator to do a solution to solve an equation.
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Where do equations come from? They come from functions. They come from functions when we ask questions like,
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what is the value of the input of a function when the output is such and such?
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So in this case, when the output is 8, what is the corresponding input to this function? In this case, x.
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So one solution technique in your calculator is put the function in y1, put the output of that function that you want to create the equation from in y2,
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get yourself a proper window. In this case, I'm going to be in the first quadrant. My window is going to be in the first quadrant here.
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And you get the graph up there and you can see the intersection. Once you can see the intersection,
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then you can find the corresponding input to an output of 8. Here's an output, vertical axis, output, horizontal axis, input.
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So if I find this intersection, I know that the horizontal or the vertical is already 8 because that lines at 8, when I need to find out it's the corresponding input here.
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So that's easy to do because I can do it with the intersection command, which is under calc.
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And I press enter to the first curve, enter to the second curve, and since there's only one intersection on my screen, enter to the third one, and it'll jump right on there.
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So that tells me that x is equal to 6. That x is equal to 6 will result in f of x being 8.
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So that's one solution technique. What are other solution techniques? I could, for example, try to do this by looking at a table.
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So if I refine this well enough, I could look at a table. This is not the best way to do this. So I started 0 and increments say every 0.5.
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I can look in a table of values here. And I could look over in this end until I see 8.
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And there it is, I see 8. And I could go back to 6. But of course, if my refinement is such that I can't find a number that I'm after over here in the outputs, then I can't read backwards to the input.
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So that's the problem with using a table. It may not get you to the most accurate answer. But get you in the ballpark for sure.
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It'll get you in the ballpark for sure. But it's not going to give you the exact answer or the precise answer necessarily.
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OK, what are other solution techniques do we have? We have the quadratic formula. Why? Well, only in this case, because why? Because this is a quadratic. We can apply the quadratic formula.
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And we could do that by simply subtracting 8 from the function. So if we subtract 8 from the function, like bring this guy over, take this guy and bring it over to the other side. And that makes the constant minus 6.
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So if we bring up a quadratic solver, which you can, if you go on the internet and learn how to download and put on your calculator, here I've got two different ones. I'm going to use this one.
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And here I'm going to ask it to pick the ABC form. So if I put in 0.5 and minus 2. And I'm not going to put in 2. I'm going to put in minus 6 because that's what I get after I subtract 8.
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Then I can see that I get a root at 6, which is the solution to the original equation. Also, I get the other one, which is on the outside of the first quadrant. I don't want this one, because I'm only interested in the first quadrant in this problem.
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So quadratic formula can potentially give you two roots, remember? So the root of the amended equation, where this is 0 and the 8's over here, is the same as the solution to the original equation.
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And there's even more techniques. Here's another little tricky technique. What if we get out of here, for example?
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Here's a little trick. Come in here and go to your equation. Subtract off the output that you were trying to achieve.
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In this case, 8. And then we're going to call up solver. I'm not going to go into a big explanation of solver. There are other videos that teach you how to use solver.
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So we're going to load solver up with y1 here. So we're going to go math and 0 is solver. And we're going to go scroll up here, just in case you forget.
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Clear this out. Scroll up, put in y1, which is where the function is.
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And what we're going to do is we're going to put in a guess. It's already solved. So it already knows 6. So this is going to be boring.
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Let's put in 8, for example. And then we're going to do alpha, solve, and let it find the value of 6. So it found 6. And it's going to find the value where the guess is close to.
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So for example, if I put in minus 5 here, I do alpha, solve. It's no surprise it finds the other root. Because minus 5 was closer to the minus 2 solution than it was to the 6.
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So if I put in, for example, 3, and I see alpha, solve again, it should find the one at 6. So you can do solver. Solver is already in your calculator. You don't have to download anything to do that.
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But you've got to be a little careful using solver because of the fact that you need a guess that's close to the intersection or solution that you want. And you don't end up getting something else.
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OK, those are some basic solution techniques for your calculator. The graphing solution technique is one of the most powerful and best ones. It does require that you have to learn how to properly get a window around there.
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And in the other videos I show you that using the table is a good way to get an idea of what window would be good to use.
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You're going to have to learn how to do all these things in order to make use of this solution technique, finding a window.
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And that's what's going to take in order to be a very efficient solver graphically. OK, that's it.