Final answer:
The new function after the vertical reflection, stretch, and translation of the parent function y=x² is y=-3(x-4)².
Step-by-step explanation:
To find the equation of the new function after a parent function y=x² is transformed, we need to apply the transformations step by step.
The first transformation is a vertical reflection across the x-axis, which is achieved by multiplying the function by -1. Thus, y=x² becomes y=-x².
The second transformation is a vertical stretch by a factor of 3. We multiply the function by 3 to obtain y=-3x².
The third and final transformation is a translation right by 4 units, which is achieved by replacing x with (x-4) in the function. Thus, the new function becomes y=-3(x-4)².
Therefore, the equation of the new function after reflecting it vertically across the x-axis, stretching it vertically by 3, and translating it right by 4 units is y=-3(x-4)².