One thing to be mindful of quadratics is that they come in many different forms.

Take for example, y = 2**x²** + 2**x** – 4. A quadratic whose **x²** and **x** term are visible is in its **general form **(in bold for clarity). This equation can be rewritten in two other forms shown below:

**Vertex form: **y = 2(x + ½)² – 4.5

**Standard form: **y = 2(x + 2)(x – 1)

All three forms mathematically **mean the same thing**, and that can be verified by graphing each one using a table of values. We haven’t learned how to convert from one form to another, but we will later on in the course.

Generally, the **vertex form** template looks like this: y = a(x – h)² + k, where **a** represents the leading coefficient, and **h** and **k **represents the *x* and y coordinate of the parabola’s vertex, respectively. We learned how **a** affects a parabola’s look in the previous lesson.

For example, in the equation y = 2(x + ½)² – 4.5, the vertex would be (–½, –4.5). Notice the + ½ in the equation had its sign flip when denoting the vertex.

Let’s take a quick look at how we can quickly plot a quadratic equation that’s in vertex form.

Another, less analytical example of the process is demonstrated below. The more practice, the better:

In our final example, you’ll see how to go from a **parabola** to a **vertex form** quadratic equation.

A summary chart of vertex form quadratics is shown below: