The standard form for a quadratic function is given by the function f(x)=2x^2‒8x‒24.

1) rewrite the function two equivalent forms: factored form and vertex form.

Factored form
f(x)=2(x^2-4x-12)
f(x)=2(x-6)(x+2)

vertex form
copmlete square
f(x)=(2x^2-8x)-24
f(x)=2(x^2-4x)-24
-4/2=-2, (-2)^2=4
f(x)=2(x^2-4x+4-4)-24
f(x)=2((x-2)^2-4)-24
f(x)=2(x-2)^2-8-24
f(x)=2(x-2)^2-32

factored: f(x)=2(x-6)(x+2)
vertex: f(x)=2(x-2)^2-32