Write an absolute value equation that is translated down 5 and reflected over the x-axis.
To write an absolute value equation that is translated down 5 and reflected over the x-axis, we can start with the standard form of the absolute value equation, which is |x| = a.
First, let's consider the translation down 5. This means that the equation needs to be shifted 5 units downward, which can be achieved by subtracting 5 from the absolute value equation. So far, we have |x| - 5 = a.
Next, we need to reflect the equation over the x-axis. This can be done by multiplying the entire equation by -1. Now we have -(|x| - 5) = a.
Simplifying the equation, we get -(x - 5) = a.
Therefore, an absolute value equation that is translated down 5 and reflected over the x-axis is -|x - 5| = a.