The parent function is the simplest form of the type of function given.

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 .

Add and .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

For a better explanation, assume that is and is .

The transformation being described is from to .

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 .

Simplify the right side.

Cancel the common factor of and .

Factor out of .

Move the negative one from the denominator of .

Multiply.

Multiply by .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raise to the power of .

Multiply by .

Divide by .

Multiply by .

Add and .

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.

In this case, which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when .

Reflection about the x-axis: Reflected

The graph is reflected about the y-axis when .

Reflection about the y-axis: None

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: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Describe the Transformation y=-(x+6)^2