Final answer:
To shift the quadratic function y=x² 3 units to the left and 2 units up, you modify it to the new function y=(x+3)² + 2.
Step-by-step explanation:
If you wanted to shift the equation y=x² 3 units to the left and 2 units up, you would change the equation to accommodate these translations.
To move the graph to the left, you substitute x with (x+3) because the graph of y=(x-h)² is the graph of y=x² shifted to the right by h units. To shift to the left, you add to x.
To move the graph up, you add 2 to the entire equation since this translates the graph vertically upwards by 2 units.
Thus, the new equation after shifting 3 units to the left and 2 units up would be y=(x+3)² + 2.