What is the equation of reflection of the curve $$ y=5x^{2}-7x+2 $$ about the pont (3,-3)?

The answer is explained as follows;

To get the reflection about origin , the x and y co-ordinates have to be inter-changed. Since reflection is about (3,-3), Replace x with x-3 and y with y+3.

So answer is $$ x=5y^{2}+23y+29 $$

When I plot the two curves, It doesn't look like they are reflections of one another. May be my understanding of this is wrong. Is the answer correct? If so, how?

## Best Answer

Let's use the following steps:

Applying to your question: