# How do you graph y=x^2 - 2?

Feb 13, 2016

Locate the vertex at (0, -2) and find the values for x=1 and x=-1. Answer: (-1, 1), (0, -2), (1, 1).

#### Explanation:

This is a quadratic function, so you will need at least 3 points to graph it. I suggests finding the vertex and 1 point to its left and 1 to its right. Notice that this function has some peculiarities that make the exercise easier:

• It doesn't have a $b$ term (a number multiplying x), so the vertex must be over the $y$ axis. Therefore, $x = 0$.
• The $c$ term (the one without x) is 2, so the function passes through the y axis at $y = - 2$.

The vertex is at (0, -2). So, procced to calculate the function for $x = 1$ and $x = - 1$. The result must be the same, as a parabola is always symmetric:
$f \left(1\right) = {\left(1\right)}^{2} - 2 = - 1$
$f \left(- 1\right) = {\left(- 1\right)}^{2} - 2 = - 1$

Finding other points for the graph is optional. These are enough to have a notion of the graph:
(-1, 1), (0, -2), (1, 1).
graph{x^2-2 [-2, 2, -2.5, 2.5]}