Investigate the graph of




Overlay a new graph replacing each x by (x - 4).


Replacing the 'x' with 'x-4' moves the points of the graph 4 to the right.


Now we can change the equation to move the graph into the second quadrant.

Replacing the 'x' with 'x + 4' (as opposed to 'x-4') moves the graph 4 to the left as shown above. Now adding a number greater than 5 to the -4 in the equation moves the graph up into the second quadrant as shown below. For the red graph, 10 was added to the -4 to give us 6.


Below the equation has been changed to produce a graph concave down that shares the same vertex.



The equation (found by completing the square) for the red graph is

For details on completing the square, click HERE

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