Cue Column:

• What is the standard form?
• What is the quadratic formula?
• What does the discriminant tell us?

Note Column: Standard form: $ax^2$ + bx + c = 0, a != 0. The roots are x = (-b ± sqrt($b^{2-4ac}$))/(2a). The discriminant D = $b^2$ - 4ac determines the nature of roots: D > 0 gives two distinct real roots, D = 0 gives two equal real roots (repeated root at -$\frac{b}{2a}$), D < 0 gives two complex conjugate roots alpha ± i*beta.

Summary: Every quadratic equation is completely characterized by three parameters (a, b, c). The discriminant is the single number that determines root nature.