X and Y Value Charts

How to use this chart to graph your parabola

Quadratic or Linear?

To find whether your relation is linear or quadratic, a chart can be used.

First Differences

As you may remember, if a relationship has the same first differences in the X and Y value chart, then it is a linear relationship.


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Second Differences

However, if a relationship does not have the same first differences, you must move on to what is called second differences. Here, you find the differences of the FIRST DIFFERENCES. If it has the same second differences, then it is a quadratic relationship


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Mapping Formula

To gather information from your equation to put into a chart, the mapping formula can be used:

(x+h) , (ay-k)

Here, you plug in your h, k and a values.


For example:

y= -0.5(x+3)^2 + 3

This equation will turn into:

(x - 3) , (-0.5y+3)

*Remember that h will have the opposite sign*

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How Do I Turn My Equation into a Chart?

After plugging the equation into the mapping formula, you can make your chart. But in order to do this, you must use the basic quadratic function! (Also known as y=x^2). One chart will be the basic quadratic equation while the other chart can be the chart of your equation.


After doing so, plug in the mapping formula points into the basic parabola chart and solve it. The outcome will be your new chart to graph! Visual steps are provided below.

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