This week I am choosing to write about how to graph the standard form (or vertex form) function . Something I was confused with at first was how this was compared to the general form function , I later learnt they share different meanings.

The value of a in the standard form function will determine if your parabola will be congruent or not to the parent function . A way that I found was easier to determine if it’s congruent or not is: if the coefficient is not a 1 then it’s not congruent. The value of a also will determine if the parabola will stretch or compress…

 

Finally the a value will determine if the vertex is a minimum or maximum and if the parabola will be open faced or down faced.

For this will determine the horizontal translation of the vertex, meaning will the x point of the vertex be to the left or the right from the 0 point on the graph. A trick that really helps for me to determine whether it will move to the right or left is: if the number is positive if will move to the left, and if it’s negative it will move to the right.

Finally the q value symbolizes the vertical translation of the vertex, meaning will the y point of the vertex be moving up or down. It’s pretty self explanatory, if the number is positive it moves up and if it’s negative it moves down.

Example:

First we know that the value of a is a positive 1 so, that will mean that the parabola is congruent to it will also tell us that the vertex is a minimum (open faced). Then the has a -1 meaning that there will be a horizontal of +1 to the right. Then the +2 means there will be a vertical translation of up 2.

We can also get the vertex from this function. If we take the horizontal and vertical translation and combine them we will get the vertex.

(1,0) -> (1,2)

When graphing the function, it will be easy… since we know the parabola is congruent to the parent value, when finding the points all you need to do is: up 1 over 1, up 3 over 1, up 5 over 1, etc.