I do NOT understand how to do this. Can someone explain in full detail/step by step how to do it? Which points in the end would I graph? (for each problem)
1) y > -x^2 -10x
2) y< 4x^2+8x+4
3) y>x^2-3x-18
$\displaystyle y > -x^2 -10x \implies y> -x(x+10)$
Solving gives us $\displaystyle x = 0,-10$ which serve as the x-axis intercepts for the inverted parabola. Graph the parabola and you have two reigions on your plane, we now have to decide which region is required.
So choose a point anywhere i.e. $\displaystyle (-5,0)$ and substitute into the equation.
If this statement is correct then this point falls in the required region, otherwise if false, reject this region and choose the other.
$\displaystyle 0 > -(-5)^2 -10(-5) \implies 0 > -25+50 $ which is false so reject this region.