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Identify the parent functions and transformations.

y= (1/4x-3/4)² - 2
Parent function: Quadratic
The function is ____vertically
shifted____by____units,
and shifted ____by____units.

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Final answer:

The quadratic function y = (1/4x - 3/4)² - 2 is compressed horizontally by a factor of 1/4, shifted right by 3 units, and shifted downward by 2 units.

Step-by-step explanation:

The function provided is y = (1/4x - 3/4)² - 2. In this expression, the parent function is the quadratic function which is typically written in the form y = x². The given function includes several transformations from the parent function.

First, there is a horizontal compression by a factor of 1/4, as seen by the coefficient 1/4 before the x in the equation. Second, the function is horizontally shifted to the right by 3 units, which we can tell from the (x - 3) term within the squared expression (remember that a negative sign inside the parentheses indicates a rightward shift). Finally, the function is vertically shifted downward by 2 units, indicated by the -2 at the end of the equation.

To summarize, the function is compressed horizontally by a factor of 1/4, shifted horizontally to the right by 3 units, and shifted vertically downward by 2 units.

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