Use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.

Answer:[tex]y=-(x+1)^2+2[/tex].Step-by-step explanation:This is a parabola so it's parent is [tex]y=x^2[/tex].Let's described what happened to get from the parent to this.The graph has been reflected so we will have [tex]y=-x^2[/tex].The graph has been moved left 1 and up 2 so this gives us:[tex]y=-(x-(-1))^2+2[/tex].Simplifying this gives us [tex]y=-(x+1)^2+2[/tex].Let's see if a few points we can identify can help confirm or convince you.Some points I see that cross nicely are:(-3,-2)(-2,1)(-1,2)(0,1)(1,-2)Let's check them and see.[tex]y=-(x+1)^2+2[/tex] with [tex](x,y)=(-3,-2)[/tex]:[tex]-2=-(-3+1)^2+2[/tex][tex]-2=-(-2)^2+2[/tex][tex]-2=-4+2[/tex][tex]-2=-2[/tex] is true so (-3,-2) does satisfy [tex]y=-(x+1)^2+2[/tex].[tex]y=-(x+1)^2+2[/tex] with [tex](x,y)=(-2,1)[/tex]:[tex]1=-(-2+1)^2+2[/tex][tex]1=-(-1)^2+2[/tex][tex]1=-1+2[/tex][tex]1=1[/tex] is true so (-2,1) does satisfy [tex]y=-(x+1)^2+2[/tex].[tex]y=-(x+1)^2+2[/tex] with [tex](x,y)=(-1,2)[/tex]:[tex]2=-(-1+1)^2+2[/tex][tex]2=-(0)^2+2[/tex][tex]2=0+2[/tex][tex]2=2[/tex] is true so (-1,2) does satisfy [tex]y=-(x+1)^2+2[/tex].[tex]y=-(x+1)^2+2[/tex] with [tex](x,y)=(0,1)[/tex]:[tex]1=-(0+1)^2+2[/tex][tex]1=-(1)^2+2[/tex][tex]1=-1+2[/tex][tex]1=-1[/tex] is true so (0,1) does satisfy [tex]y=-(x+1)^2+2[/tex].[tex]y=-(x+1)^2+2[/tex] with [tex](x,y)=(1,-2)[/tex]:[tex]-2=-(1+1)^2+2[/tex][tex]-2=-(2)^2+2[/tex][tex]-2=-4+2[/tex][tex]-2=-2[/tex] is true so (1,-2) does satisfy [tex]y=-(x+1)^2+2[/tex].All the mentioned points satisfied our equation:[tex]y=-(x+1)^2+2[/tex]