# How do you classify y = x^2 + 1?

Parabola

#### Explanation:

The given equation

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

${x}^{2} = y - 1$

The above equation is in form of upward parabola: ${x}^{2} = 4 a y$ which has

Vertex $\left(x = 0 , y - 1 = 0\right) \setminus \equiv \left(0 , 1\right)$

Axis of symmetry: $y - 1 = 0$

Directrix: $y - 1 = - \frac{1}{4}$

$y = \frac{3}{4}$