EMT 668 - Algorithms & Computers


Kimberly N. Bennekin

The following is the graph of .

i) Overlay a new graph replacing each x by (x - 4). The following is the graph of (right) and (left).

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

The standard form for the equation of a parabola is


where (h,k) is the vertex of the parabola. To move the graph into the second quadrant, we would have to move the vertex into the second quadrant by making h<0 and k>0. If we write

in standard form we get


where the vertex is (13/4, -41/8) which lies in Quadrant IV. To move the vertex into Quadrant II, we change the equation to


which moves the vertex of the parabola to (-13/4, 41/8).

The graph of

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

If a>0, the parabola is concave up. If a<0, the parabola is concave down. If we take the identical
equation and change a from 2 to -2, we will flip the parabola down. This will not change the vertex.

The graph of .

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