Question

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

Answer 1

Find `y` for some `x` values (including the vertex and the x and y intercepts, as a minimum); plot the corresponding points on the Cartesian plane; connect the points with a smooth parabolic curve.

Explanation:

The y-intercept (when `x=0`) occurs at `(0,-2)`

Since `(x^2-x-2)` can be factored as `(x-2)(x+1)`
the x-intercepts occur at `(2,0)` and `(-1,0)`

The vertex can be found by converting the given equation into vertex form:
`color(white)("XXXX")` `y = (x-1/2)^2 -9/4`
or by taking the average x value for the x-intercepts [`(2+(-1))/2 = 1/2`] and evaluating the equation for `y`
The vertex occurs at `(1/2,-9/4)`

And the completed graph looks like:
graph{x^2-x-2 [-2.86, 4.933, -3.02, 0.874]}