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\nMaster Graphing a quadratic by converting from standard to vertex form by completing the square\n

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\n\nPublisher:\n\nBrian McLogan\n\n\n
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\nWelcome, ladies and gentlemen. So, what I'd like to do is show you how to graph a quadratic in vertex form when it's in standard form. And there's a couple different ways we can do this. Obviously, we could use some different methods to...\nWelcome, ladies and gentlemen. So, what I'd like to do is show you how to graph a quadratic in vertex form when it's in standard form. And there's a couple different ways we can do this. Obviously, we could use some different methods to graph it in standard form. But in this video, I'm going to show you how to rewrite it in vertex form. So what I did is I wrote standard form in the blue up here. And then I wrote vertex form in here.

So the way that we're going to convert this is by completing the square. Then once we complete the square and we have the equation in vertex form, we can then go ahead and identify the vertex, identify the axis of symmetry, and then we can graph it, and then determine the domain and the range. Well, we could do the domain and range without graphing it, but we want to graph it.

So to go ahead and write from standard form to vertex form, to complete the square, the first thing we need to do is contain our quadratic and our linear term. Our quadratic term is our variable squared. And our linear term is going to be with our variable to the first power. So we're just going to contain these two. Now the next thing we want to do is look to factoring out terms so our a is going to be equal to 1.

Well, you can see here a is going to be the coefficient of your quadratic term. So in this case, you can see a is 1. So we're good to go on that. All right, now the next thing we need to do is we need to find the value that is going to complete the square. About to sneeze. Bless you. Thank you. Sorry. Wow, that one, like, hurt.

So we're going to find the value that's going to create this binomial into a perfect square trinomial. And I'll get to the importance of that in just a second. So to do that, what we're going to do is take b divided by 2 and square it. Well, in our equation in standard form, our b is 12. We'll take that, divide it by 2, and square it. Again, remember to follow your order of operations. 12 divided by 2 is 6. 6 squared is 36.

OK, so we're going to add 36 inside the parentheses and outside the parentheses. Now, the whole point we want to do is add it inside the parentheses. That's going to create our perfect square trinomial. But the important thing is we need to make sure we subtract it, otherwise our function would change in value. And let's think about that in kind of, maybe, some easier terms. If you had the function f of x equals x, well, if you add 1, now that's a different function.

But if you take f of x equals x and you add 1 and subtract 1, adding 1 and subtracting 1 just undo each other. It's still going to produce the same function, f of x equals x. So if I'm going to add 36, I have to make sure I also subtract 36. But just the importance is we want to make sure we add that 36, that value of b divided by 2 squared, inside the parentheses, because now that creates a perfect square trinomial, where our first term and our last term are squared terms.

And what's important about that is we can easily factor this into a binomial squared. Because if we were going to factor this, we'd say what two numbers multiplied give you 36 but then add to give you 12. Well, that is going to be x plus 6 times x plus 6, which is the same thing as x plus 6 squared. And then plus 35 minus 36 is going to be a negative 1.

Now, what's nice about this is now we have taken our equation in standard form and rewritten it in vertex form. And what's nice about vertex form is we can now understand exactly what the vertex is, because the vertex is simply just hk. Now, remember the formula is x minus h, x minus h. So whatever I'm subtracting from x is going to be my h. Well, in this case, I'm not subtracting anything. However, I could rewrite this as x minus a negative 6. Therefore, then, I would be subtracting from 6. So if it's x minus negative 6, it's the same thing as x plus 6. Hopefully you can reason, then, that h is a negative 6, and k is going to be a negative 1.\n
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Media Length
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17:46
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Grade
12th - Higher Ed
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Subjects
Math
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Media Type
Instructional Videos
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Source:
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\nBrian McLogan\n\n
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Date
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2015
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Language
English
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For Teacher Use
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Concepts

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graphing, vertex, standard form, distributive property, infinity, terms, symmetry, completing the square, axis of symmetry
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maths, how to, convert, converting, standard form to vertex form, graphing quadratic standard to vertex form, how master the graphing form, converting from standard to vertex form, standard, quadratic, form, completing, vertex form, algebra, complete the square, learn how to convert between standard and vertex form, convert equation, math help, convert quadratic equation, parabola, الرسوم البيانية, help me with math, linear term, lowest point, parent graph, negative infinity, quadratic term, important thing, axis symmetry, term, point, lowest, negative, gonna, important, ladies, axis, coordinate, thing, change, nice, make, kind, factor
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