What is the axis of symmetry and vertex for the graph y = x^2 - 2?

Feb 29, 2016

axis of symmetry is x = 0
vertex (0,-2)

Explanation:

The graph of $y = {x}^{2} \text{ is symmetrical about the y-axis}$
and has it's vertex at the origin (0,0) as shown below.
graph{x^2 [-10, 10, -5, 5]}
The graph of $y = {x}^{2} - 2 \text{ is the graph of } y = {x}^{2}$

but translated by $\left(\begin{matrix}0 \\ - 2\end{matrix}\right) \text{ moved 2 units down vertically}$

It is still symmetrical about the y-axis

hence axis of symmetry is x = 0 .

and vertex at (0,-2) as shown on graph.
graph{x^2-2 [-10, 10, -5, 5]}