In this applet we will explore how to change an equation to shift its graph up or down or left or to the right or left. This can help us spotting familiar graphs in new positions. This will also help us graph unfamiliar equations more quickly.

To shift the graph of a function y=f(x) straight upwards, we add a constant to the right hand side e.g. by adding 2 to the right hand side of the formula y = x

To shift the graph of equation y = f(x) straight down, we subtract we add a negative constant to the right hand side of the formula y = f(x)

To shift the graph of y = f(x) left or right , we add positive or negative constant to x respectively e.g. if by adding 2 to x in y = x

In general we can say

To shift the graph of a function y=f(x) straight upwards, we add a constant to the right hand side e.g. by adding 2 to the right hand side of the formula y = x

^{2}we get y = x^{2}+2 and the graph is shifted up by 2 units.To shift the graph of equation y = f(x) straight down, we subtract we add a negative constant to the right hand side of the formula y = f(x)

To shift the graph of y = f(x) left or right , we add positive or negative constant to x respectively e.g. if by adding 2 to x in y = x

^{2}to get y = (x+2)^{2}, shifts the graph 2 units to the left.In general we can say

- y = f(x) + b , shifts the graph up by b units if b > 1 or shifts it down by |b| units if b <0
- y = f(x-a) , shifts the graph right a units if a > 0 or shifts it left |a| units if a<0.

A good example of math didactics!

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