Sketch the graph y^2 + 12x = 2y - 13 Find its vertex.

pramodpandey | Student

We have given


shift the variables and we have


make lhs perfect square so ,we can write



Which is equation of parabola and defined if




parabola is open left i.e second and third quadrant .


`vertex`  is  (-1,1)


oldnick | Student

What have we to do with?






`x=0 `    not for real  value of `y`

`y=1+-2i sqrt(3)`

`y=0`    `x=1`

explicit function   `y=y(x)`  defined for  `x>=1`

We note  function hasn't critical points, indeed:


that never will be like 0.

Never if we  concern about original function:


we wl lfaound critcal points:

Indeed:     `(del f)/(del y) =2(y-1)`   zero for `y=1` 

but `(del f)/(del x)=-12`  that won'tever be zero.