The problem in the image asks to find the equation of a curve that is mirrored (reflected) across the x-axis and y-axis. The original curve is given by:

$y = x^2 - 8x - 4$

Steps to solve:

1. Reflection over the x-axis: To reflect a curve over the x-axis, we multiply the $y$-coordinates by $-1$. So the equation becomes:

   $y = -(x^2 - 8x - 4)$ Simplifying:

   $y = -x^2 + 8x + 4$

2. Reflection over the y-axis: To reflect a curve over the y-axis, we replace $x$ with $-x$. Applying this to the above equation:

   $y = -(-x)^2 + 8(-x) + 4$ Simplifying:

   $y = -x^2 - 8x + 4$

Thus, the equation of the curve after reflection over both the x-axis and the y-axis is:

$y = -x^2 - 8x + 4$

Would you like any further explanation or details? Here are some related questions to explore:

1. What is the general rule for reflecting functions across axes?
2. How does completing the square affect the transformation of quadratic equations?
3. Can a curve be reflected across any line other than the x- and y-axes?
4. What happens when we reflect a curve across both the x- and y-axes in different orders?
5. How can we find the vertex of the original and reflected curves?

Tip: To reflect a function across the x-axis, multiply the whole function by $-1$. For reflection across the y-axis, replace $x$ with $-x$.