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

Aug 5, 2018

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#### Explanation:

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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)

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:

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.