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

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Answer 1 · 2018-08-05T02:05:54

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Please read the 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)

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.

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