Final answer:
The standard quadratic function x² is shifted 3 units to the right and 4 units down is represented by the equation y = (x - 3)² - 4.
Step-by-step explanation:
The equation of the standard quadratic function x² which is shifted 3 units to the right and 4 units down can be found by adjusting the variables in the function's equation to account for the horizontal and vertical translations. The horizontal shift is represented by replacing 'x' with '(x - 3)' since the graph is moving to the right. The vertical shift down is shown by subtracting 4 from the entire function. Therefore, the new equation after applying these transformations is:
y = (x - 3)² - 4To find the equation of a quadratic function that is shifted 3 units right and 4 units down from the standard quadratic function x², we need to replace x with (x - h) to shift it right by h units and replace y with (y - k) to shift it down by k units. So, the equation of the function would be (x - 3)² - 4.
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