Quadratics

Graphing Vertex Form

 

Now that we have learnt about the vertex form, and all the different components in the equation. Let us now take a look at how we would graph equations given in vertex form. Please take a look at the video below to learn more about how to graph in vertex form:

 

                                                                                                   

                                                                                      Video: How To Graph In Vertex Form?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary: Whenever you are graphing in vertex form, you have to know the step pattern of: (1, 4, 9, 16...) which represents the graph                            y=x^2, as it serves as the basic foundation. This step pattern indicates that you go over 1 and up 1 from the vertex, to graph your                      first point. Then, in order to graph your second point, you go over 2 and up 4 from the vertex. This pattern continues onwards for                        as long as you want, but when graphing in vertex form, it is ideal that you graph approximately five points (including the vertex). If                    you were now asked to graph the following equation in vertex form: y = -2(x-1)^2+3, you would first identify the vertex, which in                      this case is (1,3). Before going any further, you would graph the vertex. Then, you would take your a-value, which in this case is                        -2, and multiply it by the original step pattern to get your new step pattern. Through mathematical calculations, you get your new                    step pattern: (-2, -8, -18...). ***The negative sign indicates that instead of going up after moving over from the vertex, you go                          down instead.*** Hence your new step pattern would read: over 1 from vertex and down 2 (first point), over 2 from vertex and down 8

             (second point) etc. Therefore, this is the process of graphing in vertex form.