Chapter P - P.1 - Graphs and Models - Exercises - Page 8: 63

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.

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