# Describe the Transformation f(x)=5/3x^2

The parent function is the simplest form of the type of function given.
The transformation being described is from to .
Find the vertex form of .
Combine and .
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 .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the value of using the formula .
Simplify each term.
Raising to any positive power yields .
Combine and .
Multiply by .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply by .
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.
In this case, which means that the graph is not shifted to the left or right.
Horizontal Shift: None
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 .
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: Stretched
Compare and list the transformations.
Parent Function:
Horizontal Shift: None
Vertical Shift: None