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Vertical translationrule

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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:

Vertical translationexamples

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:

Vertical translationequation example

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The Tilt Platform is the perfect accessory for levelling your camera when you position your slider on an angle. It gives time-lapses photographers and filmmakers the ability to create unique vertical shots while keeping your camera perfectly level and can be used with manually operated sliders or with motion control.

Vertical translationmath

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Vertical translationequation

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:

Vertical translationgraph

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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:

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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: