convert function rule f(x)=-5(x-6)(x+2) to canonical form

To convert the given function f(x)=−5(x−6)(x+2) to its canonical form, you need to expand and simplify the expression. The canonical form is typically the expanded form of the function. Here's how you can do it: 1. Start by using the distributive property to expand the expression inside the parentheses $$ f\left(x\right)=-5\left(x^2+2x-6x-12\right) $$ 2. Combine like terms within the parentheses: $$ f\left(x\right)=-5\left(x^2-4x-12\right) $$ 3. Distribute the -5 to each term within the parentheses: $$ f\left(x\right)=-5x^2+20x+60 $$ So, the canonical form of the function is $$ f\left(x\right)=-5x^2+20x+60 $$