This week we spoke about graphing quadratic equations and learning the vocabulary of graphing parabolas.

The basic parabola equation looks something like y= x²

You know the equation is a parabola because the x is squared, and by knowing and looking at what the numbers in the equation tell you, you can determine where to parabola’s exact location is on a graph.

If you are given an equation like y= x² +1

This means the parent parabola is moved up by 1 on the graph, you can tell this by looking at the plus on the end. If it was a two or a three, you would do the same and move it up depending on the number given. If the number was negative, you would move it downward.

If you were given a question where the x² is negative, the parent parabola would be flipped and opening downwards instead of up.

In questions like y=(x+1)²

You would use the number inside the brackets to determine if it is going left or right, and how far it will go. In this particular question, the parabola would be moving left. Though it has a positive number on the inside, we must do the opposite and move it to the left instead of the right. This is the same if it were negative, it would go right instead of left.

Then, moving on to stretch. The stretch is the number in front of the x² and would have an equation that looked like y=2x²

This means that all the points on the parabola will move up time two. So, taking the parent parabola, where the first easy point is 1. Instead, you would multiply this by 2, and now that point as transfer the two mark. We would do this for all the points, making the parabola look skinnier and stretched.

Putting this all together in an equation could look like y=3(x-2)²+5

On a graph, this parabola would be stretch by three, 2 to the right, and five up.

Another fact is that if you look at the 2 and the five of the equation, you have the ability to know that the vertex is going to be at the point (2,5)