Answer
From the graph we see that the intersection points are (0,-1) and (2,1). See the graph and see step-by-step solution for analytical check.
Work Step by Step
We read from the graph the points in which the two curves intersect and we see that they are $(0,-1)$ and $(2,1)$ ($x$ coordinate is cited 1st, $y$ the 2nd). To check this analytically we will substitute $x$ and $y$ from both points (one by one) into both of the equations and see if they become valid equalities:
For the 1st point:
$$-1=0^3-2\times0^2+0-1 =-1$$
which is correct.
$$-1=-0^2+3\times 0 - 1=-1$$
which is also correct so the 1st point is checked.
For the second point:
$$1=2^3-2\times2^2+2-1=8-8+2-1=1$$
which is correct.
$$1=-2^2+3\times2-1=-4+6-1=1$$
which is also correct so both points of intersection we read from the graph are analytically checked.
