To solve $ax^2$ + bx + c > 0 (or < 0, >= 0, <= 0):

Step 1: Find roots alpha, beta (alpha < beta) using discriminant. Step 2: If D < 0, sign is determined entirely by a: same sign as a everywhere. Step 3: If D >= 0, use the wavy curve method:

• Mark roots on number line
• Sign of f(x) alternates across roots
• For a > 0: positive outside roots, negative between roots

Solution sets:

• $ax^{2+bx+c}$ > 0 (a>0, D>0): x in (-inf, alpha) union (beta, inf)
• $ax^{2+bx+c}$ < 0 (a>0, D>0): x in (alpha, beta)
• $ax^{2+bx+c}$ >= 0 (a>0, D>0): x in (-inf, alpha] union [beta, inf)