F. Sketching the Graph
Completion requirements
F. Sketching the Graph
Without using your calculator, is it possible to sketch the graph of a quadratic function, given its equation? Yes, it is. In fact, it may be simpler than using your graphing calculator because you still must provide the same information on the graph. When graphing, please follow the Graphing Standards for Students.
Given the vertex form of a quadratic function, you can determine the coordinates of the vertex \((p, q)\). Use a table of values to find other points to plot to ensure your sketch is complete and accurate. For example, you could select two \(x\)-values on either side of the vertex, and then evaluate the function for each. The result would be four points on the graph of the function, plus the vertex. You may also start by using your graphing calculator. If you elect to use your calculator, you must still plot at least five points. To find points to plot, use the table of values feature on the calculator.
Graphing Standard for Students
- Plot a minimum of three ordered pairs for linear functions; two points determine a line, and the third is your check point.
- Plot an appropriate number of ordered pairs to ensure that the shape of non-linear functions can be determined.
- Label the \(x\)- and \(y\)-axes.
- Include an appropriate scale on the axes.
- Title the graph, where necessary.
- Define the line/curve with equation/function beside or near it.
- Apply arrows on the ends of the graph of the function, where necessary.
- Plot and label the \(x\)- and \(y\)-intercepts, if applicable.
- Label the vertex, if applicable.
- Include asymptotes, open circles for points of discontinuity, and end points, where applicable.
- When a graph is to be sketched, the shape of the graph is determined by important features such as asymptotes, maximum and minimum points, intercepts, etc. on an appropriate scale. All important features must be labelled.
Given the vertex form of a quadratic function, you can determine the coordinates of the vertex \((p, q)\). Use a table of values to find other points to plot to ensure your sketch is complete and accurate. For example, you could select two \(x\)-values on either side of the vertex, and then evaluate the function for each. The result would be four points on the graph of the function, plus the vertex. You may also start by using your graphing calculator. If you elect to use your calculator, you must still plot at least five points. To find points to plot, use the table of values feature on the calculator.