Kathy Radford

EMAT 6680

Assignment 2, #3

First, we will look at the graph of the parabola:

And now see what happens when x is replaced by (x-4):

The -4 translates the graph horizontally 4 units.

Next, we want to change the equation to move the vertex of
the graph into the second quadrant.
Since the vertex is below the x-axis by a little over 5, we could just
add 6 to the right side of the equation, and move the entire parabola up 6
units, but instead, let Ôs convert the equation to vertex form, and we can then
move the vertex to any point we choose.

To convert to vertex form, first we complete the square on
the right side of the equation:

Or, simplified

Which shows that the vertex is

We can move the vertex anywhere now, for example, to

Finally, by changing the sign of the coefficient of the term, we can
produce a graph of a parabola with the same vertex, but opening down: