Translating a Given Quadratic Equation to a Different Quadrant

by Amy Benson

Again, we begin with the equation

It is important to note that the vertex of this equation lies in Quadrant III. The vertex (-0.75, -5.125) has a negative x value as well as a negative y value. In order to "move" the graph into Quadrant II, the vertex needs to keep a negative x value but the y value needs to be positive. For simplicity, we will not change the x coordinate of the vertex with our translation to move the graph. Let us replace the current y coordinate of the vertex with +4. Thus, the new equation is

Let us now refer to the graph

We have successfully translated the vertex into the second quadrant. Now, we must decide if this indeed qualifies as a move into the second quadrant. What happens if we also alter the x coordinate of the vertex . Let's try

This is a horizontal shift to the left of 11.75 units.

Here, we see that the graph is unquestionably located in the second quadrant.

Our final translation vector is <-11.75, 9.125>.