What if an inequality is non-linear?

Question

 Decide with your team how to graph the y<x^2-4x+3 on graph paper.

Answer 1

Solve it the same way as a linear inequality.  

 

First graph the equation y = x^2 - 4x + 3 as a dotted line since it is a strict inequality.  This is a parabola that opens upward with vertex at (2,-1) that also goes thru the points (0,3), (1,0), (3,0) and (4,3).  Then pick a point on either side of the parabola and check to see if the inequality is true.  For example, the origin (0,0) lies below the parabola and if we plug (0,0) into the inequality we get 

 

0 < 3 

 

which is a true statement, so the inequality is true for all points below the parabola.  So shade in that region of the graph and you are done.  

 

If you pick a point above the parabola, like (0,6), and plug into the inequality you will get 

 

6 < 3 

 

which is a false statement so the inequality is false above the parabola.