Graph the parabola
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.
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.