What I learned this week in functions is vertical and horizontal translation. Knowing what the vertical and horizontal translation can help quickly find the vertex.

 

The vertical translation helps you find the y coordinate of the vertex. The vertical translation is the constant in a function.  The examples below show the function and how it would look when graphed. The vertex coordinates below are (0, 10) and (0, -3).

 

The horizontal translation determines the x coordinate of the vertex. Combining both the horizontal and vertical translation, you will be able to find the coordinates of the vertex. The horizontal translation is determined by the constant that is being added or subtracted from x. (x +/- b)^2. The opposite value of b is the horizontal translation, what I mean by this is that if you have a number three inside the bracket, your horizontal translation will be negative three. The examples below demonstrate this. The vertex coordinates below are (3, 2) and (-8, 4).