Final answer:
To translate the equation y=2(x-1)²+4 down by 1 unit and left by 5 units, the new equation will be y=2(x+4)²+3.
Step-by-step explanation:
The student's question involves translating the quadratic equation y=2(x-1)²+4 by 1 unit down and 5 units to the left. To translate the graph of this equation, we need to adjust the equation to reflect these translations.
Translating 1 unit down means we have to subtract 1 from the entire function, converting it to y=2(x-1)²+3. Similarly, translating 5 units to the left involves adding 5 to the x-variable within the parenthesis, resulting in y=2(x-1+5)²+3 or y=2(x+4)²+3 after simplification.
The new transformed equation after applying the translations will be y=2(x+4)²+3.