Example 3

Sketch the graph of the function .

Step 1: Find the zeros of the function, which will give the x-intercepts of the graph.

Plot the x-intercepts.

Step 2: Find the y-intercept.

This occurs when x = 0.

Plot the y-intercept.

Step 3: Find the equation of the axis of symmetry.

Using the x-intercept values, locate the equation of the axis of symmetry by finding the halfway point between them. Recall that in the previous Lesson, this was done by finding the average of the x-intercepts.

The equation of the axis of symmetry is x = −0.5.

Step 4: Find the vertex.
Since x = −0.5 is the axis of symmetry, f(−0.5) is the y-coordinate of the vertex.

So, the vertex is at (−0.5, 40.5). Plot the vertex.

Step 5: Use a parabolic shaped curve to connect the points.

Note that in the factored form, , the GCF of −2 tells you that the graph will open down. This was confirmed by the location of the vertex, y-intercept, and x-intercepts.

Sometimes the factored form of a quadratic function has two identical factors, such as . In this situation, the graph of the function will have only one x-intercept, at x = 3 .

Please refer to Page 338, Example 1, of Principles of Mathematics 11 for another example of graphing quadratic functions.