Apply what you have learned in this skill sheet regarding transformations. Write the equation of a quadratic function that has been transformed in the each of the ways described in parts $()$ and $(6)$ below. Write equations in $f(x)=$ form. After writing an equation check your answer using a graphing program and graph below. Be sure to label the vertex as an ordered pair. Does your graph match the description?

$($a$)$ Flipped upside down and shifted to the right $3$ units and down $2$ units.

$f(x)=$

$($b$)$ Stretched vertically by a factor of $4$ and shifted left $6$ units and up $5$ units.

$f(x)=$