How to find domains satisfying quadratic inequalities?
When you have a quadratic inequality the first step is to factorize it as if trying to solve a quadratic equation. If the equation is not easy to factorize, then complete the square or use the quadratic formula(both in GCSE syllabus).After factorizing the quadratic equation use the x's found to sketch a graph. Quadratic functions always give a parabola, and if the coefficient of x2 is positive the the parabola is U shaped, if the coefficient is negative then its upside down. Place the x's found as x-axes intersection with the curve. If inequality was greater than or equal to zero choose from x-axes and above. If it was less than or equal to zero choose from x-axes and below. (Because on x-axes y=0). If inequality didn't include equality then draw a dotted curve and don't include points of intersection. (Another question could also be how to complete the square in the first place)
