EMT 668 - Algorithms & Computers

ASSIGNMENT 2, #6

by
### 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 .

###