Question

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

Answer 1

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(1)=(1)^2-2=-1`
`f(-1)=(-1)^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]}