# How do you graph and label the vertex and axis of symmetry of y=2(x+1)^2+1?

$\left(- 1 , 1\right)$ & $x = - 1$

#### Explanation:

The given equation:
$y = 2 {\left(x + 1\right)}^{2} + 1$

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

${\left(x + 1\right)}^{2} = \setminus \frac{1}{2} \left(y - 1\right)$

Comparing above equation with standard form of upward parabola ${X}^{2} = 4 A Y$ we have

$X = x + 1 , \setminus Y = y - 1 , \setminus A = \setminus \frac{1}{8}$

Now, the vertex of standard parabola: ${X}^{2} = 4 A Y$ is

$\left(X = 0 , Y = 0\right) \setminus \equiv \left(x + 1 = 0 , y - 1 = 0\right) \setminus \equiv \left(x = - 1 , y = 1\right)$
hence, the vertex of given parabola is $\left(- 1 , 1\right)$

Now, the axis of symmetry of standard parabola: ${X}^{2} = 4 A Y$ is

$X = 0$
$x + 1 = 0$
$x = - 1$

Hence the axis of symmetry of given parabola is $x = - 1$