How do you graph y = x^2 - x - 2y=x2x2?

1 Answer
Jul 23, 2015

Find yy for some xx 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=0x=0) occurs at (0,-2)(0,2)

Since (x^2-x-2)(x2x2) can be factored as (x-2)(x+1)(x2)(x+1)
the x-intercepts occur at (2,0)(2,0) and (-1,0)(1,0)

The vertex can be found by converting the given equation into vertex form:
color(white)("XXXX")XXXXy = (x-1/2)^2 -9/4y=(x12)294
or by taking the average x value for the x-intercepts [(2+(-1))/2 = 1/22+(1)2=12] and evaluating the equation for yy
The vertex occurs at (1/2,-9/4)(12,94)

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