SOLUTION: I now have a better understanding of graphing, but need a litte help on this one. Maybe I have not mastered the tool yet. Could you please graph: x=-y^2+2y-1 Thank you ver

Algebra ->  Linear-equations -> SOLUTION: I now have a better understanding of graphing, but need a litte help on this one. Maybe I have not mastered the tool yet. Could you please graph: x=-y^2+2y-1 Thank you ver      Log On


   

Question 99121: I now have a better understanding of graphing, but need a litte help on this one. Maybe I have not mastered the tool yet.
Could you please graph:
x=-y^2+2y-1
Thank you very much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x=-y%5E2%2B2y-1 Start with the given equation

x=-%28y%5E2-2y%2B1%29 Factor out a negative to make the first coefficient equal to 1


x=-%28y-1%29%28y-1%29 Factor the right side (note: if you need help with factoring, check out this solver)


x=-%28y-1%29%5E2 Rewrite -%28y-1%29%28y-1%29 as -%28y-1%29%5E2


-x=%28y-1%29%5E2 Multiply both sides by -1


0%2B-sqrt%28-x%29=y-1 Take the square root of both sides


1%2B-sqrt%28-x%29=y Add 1 to both sides


So our equation breaks into two parts


y=sqrt%28-x%29%2B1 or y=-sqrt%28-x%29%2B1


So the first part y=sqrt%28-x%29%2B1 looks like this


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28-x%29%2B1%29+


and the second part y=-sqrt%28-x%29%2B1 looks like this



+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-sqrt%28-x%29%2B1%29+


Putting them together we get


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28-x%29%2B1%2C+-sqrt%28-x%29%2B1%29+ graph of y=1%2B-sqrt%28-x%29 which is also the graph of x=-y%5E2%2B2y-1