➗ Quadratic Equations

A quadratic draws a parabola (U-shape). Where it touches the x-axis are the roots!

y = 1x² + 0x - 4

a 1

b 0

c -4

Roots (x)

±2

Vertex

(0,-4)

Discriminant b²-4ac

Nature of roots

Real & distinct

🧠 The Big Idea

General form ax² + bx + c = 0. The graph is a parabola — opening up if a > 0, down if a < 0.
The discriminant D = b² − 4ac reveals the roots: D > 0 two real roots · D = 0 one repeated root · D < 0 no real roots.
Roots by formula: x = (−b ± √D) / 2a. The vertex is the turning point.