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\nMASTER How to graph a quadratic in standard form using the formula for axis of symmetry and vertex\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 using the equation for a vertex as well as axis of symmetry. Now, I have two functions and I have two equations, and they're basically going to be...\nWelcome, ladies and gentlemen. So what I'd like to do is show you how to graph a quadratic using the equation for a vertex as well as axis of symmetry.

Now, I have two functions and I have two equations, and they're basically going to be the exact same thing. It's just a little bit different. But I'm not really sure what type of study you're doing as far as quadratic functions or quadratic equations, so the way my explanation is going to work, I'm going to change it kind of for both of those.

However, the standard form kind of applies. When you have a quadratic in standard form, you can either complete the square, rewrite it in vertex form, and graph using our transformations, or we can identify the axis of symmetry as well as the vertex.

So the main important thing here is identifying the axis of symmetry. So the axis of symmetry is so important because that's going to be the line that the graph is symmetrical about. So it also helps us because we can graph one side of the quadratic over a parabola and then flip it to graph the other side.

So the axis of symmetry is x equals opposite of b divided by 2 times a. Remember that's for all quadratics in the form ax squared plus bx plus c.

So, therefore, in this case, I basically have negative 6 divided by 2 times 1 equals negative 6 divided by 2, which equals negative 3. Therefore, my axis of symmetry is a line, x equals negative 3.

So when graphing this, that's the first thing we're going to want to do. And that's going to basically give me an understanding of where this axis of symmetry-- where this graph is symmetrical about.

So I draw out a nice little dashed line because x equals 3 creates a vertical line. So, therefore, I know that this line not only cuts my parabola in half, but also that is going to be where my vertex-- the main important point on a parabola-- that's where my vertex is going to lie.

So by using that understanding, if I know that the axis of symmetry has an x value of negative 3, well, guess what? The vertex, since it lies on the axis of symmetry, the x value of the vertex-- because the vertex is a point where the axis of symmetry's line is going to be opposite of b divided by 2 times a and then f of opposite of b divided by 2 times a.

And this is what I was talking about, the difference between equations and functions. When we talk about functions, we talk about evaluating, right? If I had f of x equals 3x plus 1 and I say f of negative 1, then you plug in negative 1 in for x. All right.

So in this case, you're taking the x value. Then you're going to plug that x value in back to your function to find the output value, because basically in this case we have an x-axis and an f of x-axis, which is basically the same output as a y-axis if we were doing an equation. Basically represents the same thing, but the notation's a little bit differently.

So, anyways, I first need to figure out what my x value is, which is negative 3. Then to evaluate the vertex, my other point, I'm just going to do f of negative 3 because that's the x value of my vertex.

So I'm plugging that into my equation. I have negative 3 squared plus 6 times negative 3 plus 9.

Well, negative 3 squared is going to be positive 9. 6 times negative 3 is negative 18 plus 9. Well, that's going to give me 0.

Therefore, my vertex is at the coordinate point 0, 0. I'm sorry. It's at the coordinate point negative 3, 0. The vertex, OK?

Now also to graph it, it's kind of helpful to, one, identify if the graph is going to be opening up or down. You can see my a is positive so I know my graph is going to be opening up. That's a good way to always check your work, make sure you're doing it correctly.

Now, to find the remaining points, there's a couple ways you can do this. I see that this is-- my a is equal to 1. So, if you remember, when we were graphing the paragraph, when a is equal to 1, basically the relationship between the rest of the point or at least a couple points in the vertex was over 1, up 1, over 2, up 4.

And that worked for a couple points, but that only works when a equals 1. Where you can see the rest of the problems here, I don't have that flexibility to be able to do that.

So one way to just kind of double check if you don't remember that is always kind of pick two points right next to your axis of symmetry. So I'll do negative 2 and negative 1. So I'll do f of negative 2 and I'll do f of negative 1.\n
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Media Length
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19:39
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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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vertex, standard form, graphing, real numbers, symmetry, opposite, infinity, values, domain, axis of symmetry, line of symmetry
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maths, how to, help me with math, how to graph a quadratic, how to graph a parabola, parabola, quadratic, equation of axis of symmetry ib math studies, ib math studies how to plot an axis of symmetry, graph, function, math help, algebra, graphing quadratic equations, quadratics, graphing parabolas, how to find the axis of symmetry, how to find the vertex, आलेख कैसे ग्राफ़ करें, how to graph quadratic in standard form, axis symmetry, couple points, equals opposite, negative infinity, axis, line, pick, multiplying, table, fraction, problem, bracket, points, point, choose, highest, represents, make, times, 2 times
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