The parabola will yield the following graph;
But what happens when we alter the variable ÒxÓ? Suppose we replace each ÒxÓ in our original equation with Òx-4Ó so that we now have . Look what happens now.
When looking at the above graph, one can see that the vertex of the graph has shifted 4 units to the right.
This function can be generalized in the form . By changing our value for ÒbÓ, the vertex moves up and down. The value of ÒbÓ shifts the graph left and right.
LetÕs suppose we change the equation of our parabola to .
The parabola above now has vertex (4,4). We can also have the same graph open downward (concave) by changing a single value in our equation.
By placing a (-) in front of the leading coefficient (2), our parabola will now open down.
We can now change the equation to produce the two graphs above that share the same vertex.