Vertical translationrule

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Vertical translationequation

Vertical translationequation example

We see here how the horizontal and vertical translations of the reference parabola can occur within the same formula. Here is a calculation for the y-coordinate of the transformed parabola when the reference parabola is horizontally translated to the right 3 units and vertically translated downward 4 units. We will work at x = 5:

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Vertical translationmath

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Vertical translationexamples

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Here's the graph for these translations. The reference parabola ( y = x2 ) is drawn in transparent light gray, and the transformed parabola which is horizontally translated 3 units and vertically translated 4 units ( y = (x - 3)2 + 4 ) is drawn in black:

Vertical translationgraph

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So, if h = 3 and k = 4, we say that the reference parabola is horizontally translated 3 units and vertically translated 5 units. Our equation for this would appear:

On being reflected from S, the rays proceed toward the eyepiece assembly. The use of reflecting components keeps chromatic aberration at a minimum. Spherical ...

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Vertical translationand horizontaltranslation

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Vertical and horizontal translations for the parabola can happen together using both h and k. So, our starting or reference parabola formula looks like this:

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You can change the value for h or k using the upper left input boxes. Press the 'Draw graph' button after you change h or k, and you will see how your change effects the graph. For more information about EZ Graph click the following link: