Finding the Vertex in Quadratic Equations

There are two forms a quadradic equation is usually presented in: Vertex Form and Standard Form. Finding the vertex is different for each of these.

Vertex form makes it easy:

All you have to do is identify h and k and you have the vertex! h is the x point of the vertex and k is the y point.

Click here for further explanation of the Vertex Form and transformations.

This link has practice problems about Vertex Form.

Standard form is just slightly more complicated:

In the case of Standard Form, the x point of the vertex will be -b/2a, and you can plug this into the original equation to solve for y.

Sometimes you will be asked to "Complete the Square" to solve for the vertex. Completing the square can also provide other information and help you graph more easily because it converts from Standard Form to Vertex Form.

Now that we have it in Vertex Form, we can see that our vertex is (1,1).

Khan Academy has some excellent practice problems about completing the square. You can select the "Show Me Now" button on the right of the page for step-by-step help. Click here for the link!