2. Graphing f(x) = ax2 + c
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How does c affect the y-value of a point on the graph of y=ax^2+c? How does it affect the x-values?
It causes a vertical translation.
If we consider the function y=ax^2+c, we can see that if c> 0 the effect of c is to add a constant quantity to every y-value of the points of the graph. If c< 0, it will subtract a constant value. However, it does not affect the x-coordinates. This causes a vertical shift of the whole graph by |c| units — up if c> 0, or down if c< 0.
As we can see, adding a constant value c causes a vertical translation.