Student Tutorial: What Is a Quadratic Function?

Instructions:

Learn about quadratic functions. Study the examples shown.

Click the arrows on the bottom to get started

Math Clip Art: Student Tutorial Title Page

Analysis of Parabolas

A parabola is the graph of a quadratic function.

You will usually see the equation of a parabola in either Standard Form or Vertex Form.

When the value of the coefficient is negative, the parabola has this orientation.

Where the parabola intersects the y-axis is the y-intercept. The y-coordinate corresponds to c in the Standard form.

The vertex is the maximum value of f-of-x when the parabola is oriented this way.

The vertex is the minimum value of f(x) when the parabola is oriented this way.

The coordinates of the vertex are found when a quadratic is written in Vertex Form.

A parabola has an axis of symmetry along the line whose x-value is found using the values of a and b from the Standard Form.

The roots of a parabola are the x-intercepts where the parabola intersects the x-axis. A parabola can have two, one, or no roots.

This is an example of a parabola with one root.

This is an example of a parabola with one root.

This math example shows the graph of a quadratic function and demonstrates the properties of the quadratic through the graph.

This math example shows the graph of a quadratic function and demonstrates the properties of the quadratic through the graph.

This math example shows the graph of a quadratic function and demonstrates the properties of the quadratic through the graph.

This math example shows the graph of a quadratic function and demonstrates the properties of the quadratic through the graph.

This math example shows the graph of a quadratic function and demonstrates the properties of the quadratic through the graph.

Use this template to explore graphs of quadratic functions in standard form.

Use this template to explore graphs of quadratic functions in vertex form.