Example

Example 1

Sketch the graph of the function .

Step 1: Determine the vertex.

The vertex is (h, k) so the vertex is (−1, −16).

Note that the vertex form is given as . In this example, however, the function is , which can be rewritten in vertex form as .

Step 2: Determine the equation of the axis of symmetry.

Use the x-coordinate of the vertex.

The equation of the axis of symmetry is x = −1.

Step 3: Determine if the function has a minimum or maximum. Since a > 0, the parabola opens up and has a minimum y-value of −16.

Step 4: Determine the y-intercept.

(0, −15)

Step 5: Graph the function.

Note that since the vertex and y-intercept are known, another point on the graph, (−2, −15), can be determined. The point (−2, −15) is a reflection of the y-intercept in the axis of symmetry (both (−2, −15) and the y-intercept are equidistant from the axis of symmetry).