SOLUTION: How do you graph {{{y<2x^2+6x+1}}} and {{{y<= -2x^2-3x-1}}} on the same graph and shade?

First draw the boudary of  which is the parabola
whose equation is just like the inequality except that an equal
sign replaces the < .  

So draw the graph of the boundary parabola,



by plotting these points (-3,1), (-2,-3), (-1.5, -3.5), (-1,-3), (0,1) 

but draw it dotted since the inequality has  and not 



The graph will be shaded somewhere BELOW this curve.

Next draw the other boundary curve by plotting the 

points (-2,-3), (-.75,-.125) ,(-1,0)

but draw it solid since the inequality has , not . 



Now we shade the part that is below both curves, since
one is  and the other .  

Shade the part indicated below where it says 
"SHADE THIS REGION"



Edwin