Graphs of QuadraticsA series of free Basic Algebra Lessons from Brightstorm online Algebra series.
Exploring Quadratic Graphs When we graph quadratic functions, we always get a parabola (or U) shape and symmetry in the table and graph. One easy way to complete quadratic graphs is to make a table of values by plugging in x-values into the function to calculate the y-value and then plotting these points. When graphing quadratics, other important terms and features include the vertex and axis of symmetry.
Graphing Quadratic Equations When graphing quadratic equations, there are a few key terms that we can identify to help us graph quadratic functions more efficiently. Instead of plugging in values, we can find specific characteristics such as the y-intercept, x-intercepts, direction, shape, vertex and axis of symmetry. When graphing quadratic equations, it is always best to initially graph the function by hand and then check your work using a graphing calculator if able.
Vertical and Horizontal Shifts of Quadratic Graphs Horizontal and vertical graph shifts occur in a graph when the graph either moves up and down on the y-axis or side-to-side on the x-axis. When a graph shifts, the vertex simply moves position but the shape stays the same. We can graph parabolas and these shifts by either using a table of values, critical points or a graphing calculator.
Dilations of Quadratic Graphs When graphing parabolas and other functions, there are certain types of graph dilations that help us graph and explore parabolas more efficiently. When graphing parabolas, dilations occur when the "a" term value is changed. If we change the "a" to a negative, the graph shifts downward instead of upward. As the absolute value of the "a" value increases, the graph becomes "steeper." If we use a fraction as the "a" value, the graph of the parabola becomes wider.
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