This section provides step-by-step examples on how to solve quadratic equations of the form $ax^2 + bx + c = 0$. You will learn to determine the best method for solving, whether it's factoring, completing the square, or applying the quadratic formula.

Vieta's formulas provide a direct relationship between the roots of a polynomial and its coefficients. For $ax^2 + bx + c = 0$ with roots $r_1$ and $r_2$, the sum of the roots is $-b/a$ and the product is $c/a$.

The discriminant ($\Delta = b^2 - 4ac$) determines the nature of the roots of a quadratic equation. It tells you whether there are two real roots, one real root, or two complex roots.

A quadratic equation must be in the form $ax^2 + bx + c = 0$ before you can solve it using most methods.