# Explaining the Concept of a Math Translation

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Math translations come up in many different contexts but are all similar. Learn the concept of a math translation with tips from an assistant mathematics professor in this free video on mathematics.

Part of the Video Series: Mathematics: Geometry & Trigonometry
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## Video Transcript

Hi I'd like to tell you about translations in mathematics. In mathematics, translations come up in many different contexts, but they all have the same flavor. A translation, if you're thinking in terms of a picture, can be just as simple as taking your picture, picking it up, and shifting it and then putting it back down. So here's an application or an example of using a translation in mathematics. That being a translation of a function. So suppose that I am asked to graph a specific function. Here I have y=x-2 squared 3. Because of the square, we know that this will basically be a parabola shape. And so I'll start off with that shape first, our basic parabola, y=x squared and that's showing here in white. Once I know the basic shape, it's just a matter of taking the different components of the translation and moving the graph around so noticing that the two is inside the square and we're subtracting. So that's going to be a horizontal translation. And it's kind of the opposite of what you would normally think. We normally think that subtraction makes things go left. But when we're talking about translations, a horizontal translation is sort of backwards. So instead of going left, we're going to go right two. So if we consider the vertex of the original parabola, it's zero zero, moving it to the right two would move it two, zero, and then the plus three on the outside tells us that we're going to move the graph upwards three units. So then we would take our vertex, move it to the right two for the horizontal translation. And because the plus three is on the outside, we would move the graph up three units for the vertical translation. This would put our final vertex at 2, 3 and we can draw the same shape graph that we have previously and that would be the final graph that we're looking for.

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