Thread: System of Quadratic Inequalities.

Sketch the intersection of the given inequalities. 1 y≥x^2 and 2 y≤-x^2+2x+4

I can do this. You get a region of overlap, which is where the solution lies. My question is, this is a bounded region, but would we still say there are infinitely many solutions since, for instance, we can take x=0, x=0.1, x=0.01, x=0.001, x=0.0001 etc...that is, we can just move to another point in the region that is such a small difference over? Or since the region is bounded, is the solution set finite?

Also,

can you get a system of quadratic inequalities with all real numbers as the solution set? I know you can if the inequalities are just multiples of one another, but is there another way?

sure the solution is not finite as you know any interval (a,b) is not finite for b>a

can you get a system of quadratic inequalities with all real numbers as the solution set? I know you can if the inequalities are just multiples of one another, but is there another way?

I think you are talking about x values if so
you can take y < x^2 , and y> -x^2 -1