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

Mar 20, 2017

#### Explanation:

As $x = {y}^{2} + 2 y + 2$

or $x = {y}^{2} + 2 y + 1 + 1$

or $x = {\left(y + 1\right)}^{2} + 1$

Hence, this is a parabola whose vertex is $\left(1 , - 1\right)$ 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 $\left(10 , - 4\right)$, $\left(5 , - 3\right)$, $\left(2 , - 2\right)$, $\left(1 , - 1\right)$, $\left(2 , 0\right)$, $\left(5 , 1\right)$ and $\left(10 , 2\right)$. Joining them forms a curve as follows.

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