One thing to be mindful of quadratics is that they come in many different forms.
Take for example, y = 2x² + 2x – 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: