Mathematics
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• 34 lessons
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• 7 week duration
• ##### Unit 4: Quadratic Relations

Most relations that you have studied in mathematics have been linear. However, many non-linear also exist in real life.

• ##### Unit 7: Trigonometry

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

Take for example, y = 2 + 2x – 4. A quadratic whose 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 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: