How to Sketch Quadratic Relations

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Sketching quadratic relationships will require you to plot information on the X and Y planes. Sketch quadratic relations

Part of the Video Series: Math Lessons
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Video Transcript

Hello my name is Walter Unglaub, and this is how to sketch quadratic relation. So if we have a quadratic relationship between our f of x and our x where this example equation we want to plot on the xy plane the firs thing we need to do is rewrite this equation in to standard form and from that form we'll be able to identify the coordinates of the vertex. So in order to write this in standard form, we want to do the operation known as completing the square. To do that I take a look at the coefficient in front of the linear x term. In this case it's negative six. And I divide it by two which gives me negative three. So I can rewrite my original f of x as x minus three squared. There's also going to be a constant out here and in order to determine that constant I need to square this number and subtract it from this original constant in the original equation. So I'm going to have negative three squared which is equal to nine and I subtract that from 11 which gives me two. So I write the two over here. Now I've rewritten my original equation in standard form and I can identify the coordinates of the vertex. In this case, this negative three indicates that the vertex has been moved from the origin three places to the right in the positive x direction. This positive two here indicates that the vertex has been moved from the origin two places in the positive y direction. So the vertex coordinates are going to be three comma two. So I identify that on this xy plane and there's my vertex. Due to the fact that this function is symmetric from the square we're going to have symmetry and we're going to be plotting a parabola where the relationship between x and f of x is quadratic on either side of the axis of symmetry which is located at x equals three. My name is Walter Unglaub and this is how to sketch quadratic relation.


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