This week in Pre Calc 11 we learned about properties of Quadratic Functions. We learned how to determine the vertex of a Quadratic function and if it is minimum or maximum, the line of symmetry, the x and y intercepts, the domain and range and we also learned how to determine if a function is going to be congruent to the parent function: Using all of these properties that we learned, we were then able to analyse Quadratic Functions written in Standard Form or as Mrs. Burton likes to call it Vertex Form, to later be able to graph them very easily. This is an example of a Quadratic Equation written in Vertex Form: This Vertex Form is also known as  Knowing what each of the different variables represents in this form can help you analyse the function and allows you to get a really good sense of what it would look like on a graph.

In Vertex Form, :

is the vertical translation, which means that it will translate either a certain number of units up or down along the y axis. It also tells us what the in the vertex is going to be.

is the horizontal translation, which means that it will translate either a certain number of units to the right or to the left, moving along the x axis. It also tells us the line of symmetry and what the in the vertex is going to be. However we must remember that the sign changes when you take the  value out of Vertex Form and put it into your vertex. Example:  the vertex for this function would be 

tells us the parabola is going to be congruent to the parent function, if it going to be a reflection or not and if it is going to be a stretch or a compression. If the value of is is a number other than 1, then the parabola will not be congruent to the parent function. If the sign is negative the parabola will have a maximum vertex, which means that it opens down and that it will be a reflection, however if positive the parabola have a minimum vertex which means that it will open up. If the value for  is a fraction then the parabola will become wider and will be a compression and if the value is a whole number, then the parabola will become skinnier and will be a stretch. Example:  in this function, the parabola will be a reflection, it will have a maximum vertex which means that it will open down and it is a stretch.

In the example that I used throughout this post, we discovered that the vertex is going to be  that it is not congruent, that it is a reflection and has a maximum vertex. If I were to graph this function with the information that I have determined, the function would look like this: