Summer Tuggle

Assignment
2.6

Graph the parabola

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

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

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

**Purple:**

**Red: **

**Blue:**

**Green:**

The
purple graph is the original function.

The
red graph is simply a shift of the original 4 units to the right.

In
order for the blue graph’s vertex to be contained in the second quadrant, the
vertex has to be shifted so that the x is negative and the y is positive. I first had to shift the parabola to the left
4 units. This is accomplished by shifting the x coordinate (hence the
x+4). Then the y value has to be
positive (hence the +4 as the “c” value).

The
green graph shares a vertex with the blue graph. It is simply concave down. This is accomplished by making the “a” and
“b” coefficient negative.