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

Jul 23, 2015

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 $\left(0 , - 2\right)$

Since $\left({x}^{2} - x - 2\right)$ can be factored as $\left(x - 2\right) \left(x + 1\right)$
the x-intercepts occur at $\left(2 , 0\right)$ and $\left(- 1 , 0\right)$

The vertex can be found by converting the given equation into vertex form:
$\textcolor{w h i t e}{\text{XXXX}}$$y = {\left(x - \frac{1}{2}\right)}^{2} - \frac{9}{4}$
or by taking the average x value for the x-intercepts [$\frac{2 + \left(- 1\right)}{2} = \frac{1}{2}$] and evaluating the equation for $y$
The vertex occurs at $\left(\frac{1}{2} , - \frac{9}{4}\right)$

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