# Describe the Transformation y=(x+2)^2-3

The parent function is the simplest form of the type of function given.
Simplify .
Simplify each term.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Subtract from .
For a better explanation, assume that is and is .
The transformation being described is from to .
Find the vertex form of .
Complete the square for .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
Simplify each term.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Subtract from .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
The horizontal shift depends on the value of . The horizontal shift is described as:
– The graph is shifted to the left units.
– The graph is shifted to the right units.
Horizontal Shift: Left Units
The vertical shift depends on the value of . The vertical shift is described as:
– The graph is shifted up units.
– The graph is shifted down units.
Vertical Shift: Down Units
The graph is reflected about the x-axis when .
The graph is reflected about the y-axis when .
Compressing and stretching depends on the value of .
When is greater than : Vertically stretched
When is between and : Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
Horizontal Shift: Left Units
Vertical Shift: Down Units