How to Graph in Vertex Form

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Graphing in vertex form is something you do when dealing with a function of the quadratic form. Graph in vertex form with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Video Transcript

Hello. My name is Walter Unglaub and this is how to graph in vertex form. So graphing in vertex form implies that there's a vertex to your figure. Usually what is meant by this is that we're dealing with a function of the quadratic form. So there's at least one term in your function that has an x squared term in it. So the general form of a quadratic function I'll write as a, where a is some parameter times x minus b squared, where b is also a parameter, plus c. A represents by how much you stretch your graph in the vertical direction, b corresponds to how far along the x direction you shift your vertex. And c corresponds to how far up the y axis you shift your vertex. So if I want to plot x squared my origin and also the vertex will be here and it will look something like this, where the axis of symmetry is along x equals zero. For this example, a more general example I can consider a is equal to 1, b is equal to 3 and c is equal to 2. So if a is equal to 1 which is the case here, then there's going to be no stretching involved. If b is equal to 3 then my vertex which was originally at the origin is going to be moved over to the right 3 places and my c means I'm going to shift my vertex up in the vertical direction by 2 points. So I'm essentially going to have x squared just in this location. And again, I'm going to have an axis of symmetry where in this case the axis of symmetry is x is equal to 3. So this is sometimes called the standard form. And the position of the vertex and the axis of symmetry is defined via the values of these coefficients of these parameters. My name is Walter Unglaub and this is how to graph in vertex form.

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