Determine an eligible candidate for comparison. This step is straightforward in most cases. Examine the graph and determine which standard function appears most like it. For example, a parabolic shaped line resting anywhere within the plane would be compared to a parabola.
Compare the transformed graph to a standard graph of the function used for comparison. In this process, determine in what directions and by how much distance the standard graph would need to be moved in order to exactly match the original graph. For example, a standard parabola would need to be moved up a distance of one to match a parabola whose lowest point is the coordinate (0,1).
Record the horizontal and vertical movements needed to make the standard graph match the transformed graph.
Place the "x" value of the standard equation in parentheses. Leave out any exponents and square roots from the parentheses. Example: f(x) = x^2 -> f(x) = (x)^2.
Adjust the function for movement in the horizontal direction. If the function must be moved to the left on the coordinate plane, add the distance required; if it must be moved right, subtract the value. Example: f(x) = x^2 -> f(x) = (x + 3)^2 (left shift) or f(x) = x^2 -> f(x) = (x - 3)^2 (right shift).
Adjust the function for any vertical displacement. Add or subtract to the outside of the term involving "x" if there is an upward shift or downward shift, respectively. Example: f(x) = (x + 3)^2 -> f(x) = ((x + 3)^2)+2 (upward shift) or f(x) = (x + 3)^2 -> f(x) = ((x + 3)^2)-2 (downward shift).