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 -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.