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

1 Answer
Aug 14, 2017

If you're familiar with parent functions, graph f(x)=x^2 and move it down the y axis two units.
The solutions are +-sqrt(2).

Explanation:

Since f(x)=x^2 is the parent function for a parabola, f(x)=x^2 -2 is just that parent moved down two units. So this is just a parabola with a vertex that is at (0,-2) instead of being at (0,0).
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(x) is the same thing as the y value, plug 0 in for f(x): 0=x^2-2. Add 2 to both sides, and you get 2=x^2. Take the square root of both sides, and +-sqrt(2)=x.