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There are several ways to solve quadratic inequalities. I will show you one way now: graphing them on the coordinate plane. We can start out with two inequalities: y>x2y > x^2 and y<4x2y < 4x^2. First, I will graph the first equation: y=x2y = x^2. Now, we can choose a random point inside the curve such as (0,4)(0, 4) and test if it fits the inequality. Since y(4)y(4) is larger than x2(0)x^2(0), we should remember that the section inside the blue curve is 'true'.

Now, let's look at the second inequality, y<4x2y < 4x^2 and its equation y=4x2y = 4x^2.

The green curve is the equation y=4x2y = 4x^2. Again, let's choose a random point inside the green curve such as (0,5)(0, 5) and test it. y(5)y(5) is actually greater than x2(0)x^2(0), so the region outside the green curve is 'true'. Therefore, the region inside the blue curve but outside the green curve is 'true' for both inequalities.

Do you get this method of solving quadratic inequalities?

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