__Manipulating
The Parabola__

Damarrio C.
Holloway

EMAT 6680 Summer
2006

Dr. Wilson

The victim of my problem is the equation:

GRAPH 1

Graph 1 is the simple parabolic
graph of my initial equation. Now we will begin the manipulation.

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

GRAPH
2

Graph 2 is the graph when each ÔxÕ is replaced by
(x-4). The new graph shifts to the
right with the same vertex as the original graph and the roots on the graphs
are equidistant.

ii)
Change the equation to move the vertex of the graph into the second quadrant.

By changing the ÔcÕ coordinate to
+2, raises the vertex of the graph to the 2nd Quadrant.

iii)
Change the equation to produce a graph concave down that shares the same
vertex.

Changing the ÔaÕ to Ô-aÕ does
create a concave downward parabolic function, but it will not necessarily
create a common vertex as seen below in graph 4. The first two equations
are the same but the new equation is . The graph does concave downward with a
tangent point of y=4.

GRAPH 4

** **

__New Equation__

GRAPH
5

Changing the terms of ÔxÕ in the
original equation produced the second function yielding the purple graph.
Going back to the instructions in part i), I began changing the x terms to give
a phase shift to the left instead of a right phase shift. Keeping the ÔcÕ
coordinate negative leaves the vertex in the bottom two quadrants, but changing
the ÔaÕ coordinate to (-), creates a downward parabolic function. In
graph 5, we see the perpendicular bisector is the line x=-0.75, and the common
vertex that they share is y=-5.125.

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