Parts of a Quadratic Function

​The graph of a quadratic function creates a U-shaped parabola.

• The vertex is the very top (max) or bottom (min) of this shape.​

• The Axis of Symmetry is a vertical line that splits the parabola in half with left and right sides matching.

• The x-intercepts are ​the points at which the parabola crosses the x-axis. There can be none of these, one of these or two of these.

Standard Form

Finding the Vertex

From the Standard Form

Example... Find the vertex of f(x).

Factored Form

Finding the Vertex

From the Factored Form

Example... Find the vertex of f(x).

Finding the Y-Intercept

From the Factored Form

Graphing the Function

In the Standard Form...

• Find the vertex

• Choose x-values immediately next to the vertex. Create a table of values and use the equation to get y-values for these points.

• Plot these points.​ Ensure that your parabola is symmetric and opens the correct direction.

In the Factored Form...​

• Find the x-intercepts

• Find the vertex

• Plot these three points and draw the U-shape. Ensure it opens in the correct direction.​