Assignment 2Sandy Cederbaum

**By replacing
each x in by (x-4),
we see that the red graph appears to be a horizontal
transformation of our original graph. The transformation shifts
the purple graph 4 units to the right.**

**Try this: Plug
in 0 for x in the purple equation. Now plug in 4
for x in
the red equation.
What do you
notice? Find another value of x for each of the above equations
that will do the same job. Can you find a value of x for each
of the above equations that will give you the SAME Y-VALUE generated
by our first trial of x=0 and x=4?**

**You should already
have a good idea of how to move a graph to the left. Think about how you might translate the
purple graph
in order to
shift it up and to the left. Change
the equation to move the vertex of the purple graph into the second
quadrant? Here
is the big hint to help you move the graph vertically...Which
variable will you ADD to or SUBTRACT from in order to make the
graph go up and down? Click
here in order to see the solution. **

**Can you change the equation to
produce a graph concave down that shares the same vertex? (Hints:
You want all
of the y-values to be OPPOSITE, and it
might be helpful to find the vertex). Click
here in order to see the solution. **

**You have now had the opportunity
to see translations of a quadratic function in a slightly different
light. The concepts that you have just worked with should help
you become a little more intuitive when faced with a problem that
involves shifting graphs around the Cartesian plane.**