The function is $\"\"$ , where $\"\"$ is the spring constant and $\"\"$ is the distance from the equilibrium.

(a) The parent function is $\"\"$ .

The graph of $\"\"$ expanded vertically, if $\"\"$ .

The graph of $\"\"$ compressed vertically, if $\"\"$ .

Therefore, the transformation is vertical.

(b)

The point is $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

The function for the potential energy is $\"\"$ .

Spring constant is $\"\"$ .

(a) Vertical transformation.

(b) Spring constant is $\"\"$ .