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.