As many students are taking Algebra II this semester, Mr. Bautista seems to be quite frustrated at a few students, who need help understanding the curriculum relating to graphing. A new topic is vertex form, one of the few formulas for graphing parabolas.

The quadratic equation looks like y= a(x-h)2+k. They can be substituted to f(x), as it means the same thing. Each letter is important because it determines how wide, thin, and tall the parabola is and the location, especially where the vertex is. The ‘a’ is the amplitude, or how wide or skinny the shape will be. If ‘a’ is larger than 1, then it would become skinnier. It would become wider if it is smaller than one, like ½. If, in any circumstance, the number is negative, it would mean the parabola would be flipped like a sad face. The ‘x’ implies it will be the x-value of the vertex. The same idea is for k, the y-value of the vertex.

Here is an example. Let's say a=2, h=3, and k =3. If we plug in the numbers the formulas would be y=2(x-3)2 +3. With what we know, the x-value is 3, and the y-value is 3, so therefore the vertex is located on (3,3). Then, a=2, which is larger than 1. So, when you create the graph, you expect it to be skinnier than the normal parabola.

If you are uncomfortable with the vertex form, you can always extend the equation, and simplify. For example, a(x-h)2+k, if you simplify, would be in the standard equation, which is y=ax+bx+c. With that, if able to, you can factor by grouping.