How do you sketch the graph of #y=(x+2)^2# and describe the transformation?

1 Answer
Aug 5, 2018

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Please read the explanation.

Explanation:

#" "#
We are given the quadratic function: #color(red)(y=f(x)=(x+2)^2#

For the family of quadratic functions,

the parent function is of the form #color(blue)(y=f(x)=x^2#

When graphing quadratic functions, there is a useful form called the vertex form:

#color(green)(y=f(x)=a(x-h)^2+k#, where

#color(green)((h,k)# is the vertex.

Data table is given below:

(both for the parent function and the given function)

enter image source here

For the parent function,

Vertex: #color(red)((h,k)=(0,0)#

For the given function,

Vertex: #color(red)((h,k)=(-2,0)#

Let us graph:

enter image source here

#color(red)(y=f(x)=(x+2)^2#

moves (shifts) the graph LEFT by 2 units.

Note on Transformation:

Hence we can observe that there is a horizontal translation.

Hope it helps.