Welcome to MPM2D0 

Graphing Vertex Form.

 

Now, we know the effect of each value in the vertex form. However, we will learn how to graph vertex form: 

 

Using table of values and the formula y=x^2 . The original step pattern of a parabola is "over one up one, over 2 up four." Usually, the vertex decides where the step pattern starts. The "a" value decides if the step pattern changes ( the "a" value is multiplied by the vertical part of the step pattern.) 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    Step Pattern:

 

 

 

 

 

Firstly, you find you h and k values and then find the vertex (x,y). In this example you it was a positive 5 though it is the opposite so it is left 5 and the k value is a negative 3, meaning down 3. This gives you the vertex of (-5, -3). And then following the " over one up one, over two up four." rule and did it to the both side and plotted points and drew a parabola which opens up.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This example differs from the first one because here we have a value meaning vertical stretch/compress to graph as well. In this example the parabola was being stretched by a factor of 3, left 7, and down 2. Vertex at (-7, -2), the pattern of y= x2. However, the vertical part of the pattern is multiplied by the "a" value. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

So when using a table of values to figure out the vertical part you simply multiply x to itself and multiply it by the a value.