Exploring
Parabolas
Erin
Mueller
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.
