This week in Pre Calc we learned more about Quadratic Functions. General – , Vertex – , and Standard. (the latter two both apply to the same form of function, they just have different names.)

In this post I’ll talk about going from Vertex to Standard and vice versa.

First if let’s start with a Vertex form function,

First we start off by dividing to get the x on it’s own (this whole process is just going to be completing the square, like we’ve done with quadratics in the past.)

once we divide the and by 3 (to factor it out) we’ll have

then we’ll take the middle term, in this case it’s 2x, divide it by 2, and square. This is the formula

Now, since we’re completing the square, you add the product of that formula to the existing equation: We’ll multiply the 3 with the -1 to take it out. which becomes $latex 3(x^2+2x+1)-75

Now, we can simplify and factor. and factored becomes y=(x+1)^2. So together our new function is y=3(x+1)^2-75$ Now we know this function has a stretch factor of 3 and can easily tell the vertex.

Now let’s go back from Vertex to General.

All we have to do is un factor our function.