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Let $m(x) = x^2 - 8x + 9\text{.}$

Write a formula for the transformation $m(-x)$ and geometrically describe the transformation.
To do this, use the blank method: write the output $x^2 - 8x + 9\text{,}$ but replace all instances of the variable $x$ with the new input, $-x\text{.}$ Remember to use parentheses when substituting this in for $x\text{.}$
Formula: $m(-x) =$
For the geometric description, remember that we are taking the opposite of the input variable, so this will affect the graph’s position in the horizontal direction.
Description: $m(-x)$ will reflect the graph of $m(x)$ over the

Write a formula for the transformation $-m(x -$ 7 $)\text{.}$
Notice that there are two changes here: Subtracting 7 from the input, and the opposite symbol outside.
First apply the inside change by replacing all instances of the variable $x$ with the new input, $x - 7\text{.}$ Remember again to use parentheses when substituting this expression for $x\text{.}$
This would leave us with:
( $)^2 -$ 8( $) +$ 9
Next, apply the outside change by putting the opposite symbol outside of this whole expression, again remembering to use parentheses.
Formula: $-m(x -$ 7 $) =$
The inside change of subtracting 7 will move the graph in the horizontal direction. The outside change of taking the opposite will affect the output values by changing their sign.
Description: $-m(x - 7)$ will shift the graph of $m(x)$ by 7 units and reflect it over the