Example 1

The function has zeros of and 1. Determine the y-intercept, the equation of the axis of symmetry, and the coordinates of the vertex. Use this information to sketch the graph.

y-intercept

The y-intercept occurs when x = 0 .

The y-intercept occurs at (0, −3).

Axis of Symmetry

The axis of symmetry is halfway between the two zeros. Averaging the two values will give the x-coordinate of the midpoint.

is the equation of the axis of symmetry.

Vertex

The x-coordinate of the vertex corresponds to the equation of the axis of symmetry. Thus, the x-coordinate of the vertex of f(x) is −0.25.

The vertex is at (−0.25, −3.125).

Sketching the Graph

Plot the points you know and draw a smooth curve through them.

Note: Although the points determined above make it clear that the parabola opens upward, a quick confirmation that for reinforces those findings.