Question

Draw the graph of `x=y^2+2y+2`?

Answer 1

Please see below.

Explanation:

As `x=y^2+2y+2`

or `x=y^2+2y+1+1`

or `x=(y+1)^2+1`

Hence, this is a parabola whose vertex is `(1,-1)` and axis of symmetry is `y+1=0`

Let us select some points around `y=-1` say `y=-4,-3-2,-1,0,1,2`

for these corresponding values of `x` are `x=10,5,2,1,2,5,10`

and draw points `(10,-4)`, `(5,-3)`, `(2,-2)`, `(1,-1)`, `(2,0)`, `(5,1)` and `(10,2)`. Joining them forms a curve as follows.

graph{y^2+2y+1+1-x=0 [-2.71, 17.29, -5.72, 4.28]}