# How do you graph f(x)=x^2-2 and identify the x intercepts, vertex?

Aug 14, 2017

If you're familiar with parent functions, graph $f \left(x\right) = {x}^{2}$ and move it down the y axis two units.
The solutions are $\pm \sqrt{2}$.

#### Explanation:

Since $f \left(x\right) = {x}^{2}$ is the parent function for a parabola, $f \left(x\right) = {x}^{2} - 2$ is just that parent moved down two units. So this is just a parabola with a vertex that is at $\left(0 , - 2\right)$ instead of being at $\left(0 , 0\right)$.
If you're not familiar with parent functions, make a table. Plug in some $x$ values and find what the associated $y$ values are.

To find the $x$ intercepts, first think about what that means. We also call the $x$ intercepts "zeros" and "solutions". These occur where the function crosses the $x$ axis. If a point is on the $x$ axis, the $y$ coordinate is zero.
Since $f \left(x\right)$ is the same thing as the $y$ value, plug $0$ in for $f \left(x\right)$: $0 = {x}^{2} - 2$. Add 2 to both sides, and you get $2 = {x}^{2}$. Take the square root of both sides, and $\pm \sqrt{2} = x$.