How do you graph quadratic functions?

Plot at least seven points from the quadratic equation, and then draw a parabolic curve through the points to make the graph. Remember that quadratic equations always show up as parabolas on graphs.

1. Plot a minimum of seven points from the quadratic equation

   Enter the integers -3 through 3 as the x-values in the equation. Calculate the corresponding y-values, and place both x-values and y-values in a T chart. Draw an x-axis and y-axis on graph paper, and graph the points.

2. Draw a provisional curve through the points

   Look at the points to see if connecting them forms a "U" shape that faces upward, downward or to one side. If the points resemble a gradually flattening line, plot more points near the flatter part of the line. Once you have enough points, draw a curve through the points to create a parabola. Draw arrows on both ends of the curve to show it continues infinitely in both directions.

3. Check your graph

   To validate the graph, take two or three points that appear on the curve but not on your T chart. Plug the x-value into the equation, and see if the corresponding y-value emerges. If it does, the graph is correct.