Answer Step-by-step explanation:
[tex]\huge\boxed{A)-1}[/tex]
[tex]The~average~rate~of~change~of~the~given~quadratic~function~on~the[/tex] [tex]interval~0[/tex] ≤ x ≤[tex]4[/tex] [tex]is~the~slope~of~the~secant~line~connecting~the~points~(0,f(0))~and~(4,f(4)).[/tex]
[tex]The~average~rate~of~change~is:[/tex]
[tex]=\frac{f(4)-f(0)}{4-0}[/tex]
[tex]Now,from~the~graph,f(0)~is~0~and~f(4)~is~-4.[/tex]
[tex]We~plug~in~these~values~to~obtain;[/tex]
[tex]=\frac{-4-0}{4-0}[/tex]
[tex]And~then,this~simplifies~to:[/tex]
[tex]=\frac{-4}{4}[/tex]
[tex]which~is~obviously:[/tex]
[tex]=-1[/tex]
[tex]Thus,~the~average~rate~of~change~for~the~given~quadratic~function[/tex] [tex]whose~graph~is~shown~on~0[/tex] ≤ x ≤ [tex]4~is~=-1.[/tex]
