In Precalc 11 this week, we continued to work on Quadratic equations and graphing them. We learned about the difference between general and standard form of the equation and how to graph equations and how to write an equation for the graph.

General form is when the equation is in y=ax^2+bx+c and y=a(x-m)^2+n is standard vertex form. To change it from general form to standard form you used what we learned last unit about completing the square to change it into standard vertex form.

If you have an equation that looks like this:

You want to first look at what each part means. There is nothing in front of the bracket meaning that there is no stretch and that the graph is opening up because it isn’t a negative. The (x-3)^2 means that there is a horizontal translation and its going to the right. The +4 means the it is a vertical translation and that it will also move up 4. By looking at the equation you can tell what the vertex is going to be, (3,4).

If you have a graph with a parabola that looks like this:

To find out the equation the first thing that you can look is to see if there is a stretch, and in this case there is a stretch on +2. Next I look for if it is undergoing any translations, which I noticed it is, both vertical and horizontal. I looked how far the vertex moved from the origin and it moved over three to the left, meaning that it will be (x+3)^2 and it moved down 5. So the final equation will be; y=2(x+3)^2-5.