Domain of \(\displaystyle{x}^{{2}}-{12}{x}\):

Solution:\(\displaystyle-∞{<}{x}{<}∞\) ;

Interval Notation: \(\displaystyle{\left(-∞,∞\right)}\)

Range of \(\displaystyle{x}^{{2}}-{12}{x}\):

Solution: \(\displaystyle{f{{\left({x}\right)}}}\Rightarrow-{36};{\left[-{36},∞\right)}\)

Axis interception points of \(\displaystyle{x}^{{2}}-{12}{x}\):

X-Intercepts: (12,0),(0,0),

Y-Intercepts: (0,0)

Vertex of \(\displaystyle{x}^{{2}}-{12}{x}\)

Vertex form is: \(\displaystyle{y}={\left({x}-{6}\right)}^{{2}}-{36}\)