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\nMASTER Graphing a quadratic function in vertex form, identify vertex, axis of symmetry and domain\n

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\n\nPublisher:\n\nBrian McLogan\n\n\n
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\nWelcome to McLogan. So what I'd like to do is show you how to graph a quadratic when it's in vertex form. Now, when graphing a quadratic in vertex form, it's very important to know two things, one, what exactly is vertex form. And I...\nWelcome to McLogan. So what I'd like to do is show you how to graph a quadratic when it's in vertex form. Now, when graphing a quadratic in vertex form, it's very important to know two things, one, what exactly is vertex form. And I guess I did not write vertex form anywhere, so let's go ahead and write vertex form right over here.

So vertex form is y equals a times x minus h squared plus k. Now, what's nice about vertex form is, we can easily identify the vertex as just h comma k. And also we can identify the axis of symmetry as x equals h. So it's really easy to be able to figure out what the vertex is as well as the axis symmetry and that's going to help us graph it.

Now, for these six examples, I'm going to graph them when a is equal to 1, which should make it even nicer and easier. So the first thing I'm going to do is, I'm going to graph what the parent graph looks like. So the parent graph is just going to be if I was just going to graph f of x equals x squared.

Now, it's very important for you to understand if you were to use a table of values, then the graph would go up over 1, up 1; over 1, up 1; over 2, up 4; over 2, up 4. Because if you plugged in some numbers, you can plug in. 1 squared is 1. If you plug in 2, 2 squared is 4. So when you go ahead and connect these, what you have is the shape of our quadratic, which we call a parabola or a lot of times people call it like the U-shaped graph. It looks like a U.

So basically what we're going to do is, we're going to identify what exactly is the new vertex and then just basically redraw that graph. Since our a is going to be 1 in all these cases, a negative 1 in a couple, but since the absolute value of a is equal to 1, there's not going to be any compression or stretching. So therefore, I'm basically just going to take this graph and move it around.

Now, the easiest way to do that is to identify the vertex. So in this example, you can see that the vertex is at 0, 0. But now when we look at our new equation, you can see that h-- I don't have a value for h, so there's no x minus anything. So therefore, h is going to be 0, and k is going to be 2 because that's what I'm adding over to my function.

So my new vertex is going to be at 0 comma 2. And we're going to want to write that out. So for this example, my vertex-- again, I'm not adding or subtracting inside the function, so my vertex is going to be 0 for h and then 2 for k. The axis of symmetry is still going to be x equals h, so therefore, that's going to be x equals 0.

So all I'm simply do is just taking this graph and shifting it up 2 units. So I'm still going to go over 1, up 1; over 1, up 1; then over 2, up 4-- 1, 2, 3, 4. And then the axis of symmetry is right there on the y-axis.

Now, in this example, you can see that I'm not adding or subtracting anything outside. See how I'm adding 2 outside the function? Here is subtracting 2 inside the function. But the other important thing to remember about this is it's x minus h. So therefore, it's x minus h, so it's x minus 2. Therefore, h is equal to 2, which is a very common mistake with students.

So therefore, I can write in the vertex is going to be 2 comma-- well, I could really just write plus 0 because I'm not adding anything-- 2 comma 0. So therefore, rather than shifting the graph negative 2, my h is actually positive 2 because it's h minus 2 or x minus h. x minus 2 to. 2 and h are equal. So therefore, it's plus 2, so therefore, I'm basically shifting this graph 2 units over.

So if I had a scale here-- 1, 2. So therefore, my new vertex is going to be at 2 comma 0. Now, all I simply need to do is follow, again, the same pattern of my parent graph. Go over 1, up 1; over 2, up 4-- 1, 2, 3, 4-- over 1, up 1, and you can always use the axis of symmetry here. The axis is x equals h, which in this case is 2.

So I can draw a nice little vertical line here, and by doing that vertical line, whatever points to the left, I can reflect over to the right. Then I just connect and make this nice little shaped U graph.

One thing that I did forget to do is talk about domain and range, and I figured that this would be a great opportunity to go and do that. So let's actually go back here real quick to this example. If we look at the black graph, the domain is going to be the set of all x values that make up that graph. Well, you can see, as this graph is going up, it's continuing to expand.\n
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Resource Details

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Media Length
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15:05
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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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Audiences
For Teacher Use
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Fine Print: Educational Use
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Concepts

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graphing, vertex, domain, range, real numbers, symmetry, infinity, transformations, axis of symmetry, line of symmetry
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math, maths, how to, learn, quadratic, graph, graph a quadratic, how to graph a quadratic, identify the vertex and axis of symmetry of a quadratic function, graphing quadratic functions in vertex form what is domain, quadratic functions in vertex form, graphing quadratic functions in vertex form what is axis of symmetry, graphing quadratic functions in vertex form what is the domain, algebra, ग्राफ़ एक द्विघात, black graph, blue graph, vertex form, negative infinity, axis symmetry, domain range, inside, negative, important, equals, axis, thing, alright, subtracting, identify, simply, shifting, left, reflect, paragraph, remember, ahead
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