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Check the degree of your polynomial. Draw the x- and y- axes. Number your graph. Calculate y = f(x) for every x. Make a graph point for each pair. Draw the graph of the polynomial. Look for the axis of symmetry. Note the axis of symmetry.
The degree (or “order”) of a polynomial is simply the largest exponent value in the expression. If the degree of your polynomial is 2 (there is no exponent larger than x2), you can find the axis of symmetry using the formula method above. If the degree of the polynomial is higher than 2, use this graphical method. Make two lines in the shape of a plus sign. The horizontal line is your x-axis; the vertical line is your y-axis. Mark both axes with numbers at equal intervals. Spacing should be uniform on both axes. Take your polynomial or function and calculate values of f(x) by putting all values of x into it. You now have pairs of y = f(x) for every x on the axis. For each (x, y) pair, make a point on the graph – vertically on the x-axis and horizontally on the y-axis. Once you have marked all the graph points, you can connect your dots smoothly to reveal a continuous graph of your polynomial. Inspect your graph carefully. Look for a point on the axis such that when a line is passed through it, the graph splits into two equal, mirrored halves. If you can find a point – call it “b” – on the x-axis that splits the graph into two mirrored halves, then that point, b, is your axis of symmetry.