Shifting of Parabola

As stated previously, the graph of y=x2 is our standard graph.

If equation is given in the format of  y = x2 + h than the graph shifts only up or down, depending upon whether the value of h is positive or negative, respectively.

Some examples are given below.


 
Now, let's look at the graphs of :
y = x2 (red)
Some equations expressed in form of :
y1 = (x + 4) 2 - 2 (green)
y2 = (x + 4) 2 + 2 (blue)
y3 = (x - 4) 2 - 2 (brown)
y4 = (x - 4) 2 + 2 (purple).
Notice that the graphs have vertices (0, 0), (-4, -2), (-4, 2), (4, -2), and (4, 2), respectively. 

Note: In all the above equations constant a which is one in above equations is 1 (a=1). That's why all parabola are facing upwards.

**ART :- 
Whenever there is a constant added to the value of y that shifting will occur along y axis or vertically.
Simultaneously when a constant is added to x than shifting will occur along x axis or horizontally.

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