Algebra 2: Quadratic Functions
Quadratic functions model parabolas — curves that appear in physics, engineering, and nature. Master factoring, the quadratic formula, and interpreting graphs.
Key Concepts
Standard Form
y = ax² + bx + c. The coefficient a determines direction (up if a>0, down if a<0) and width. The vertex is the maximum or minimum point.
Factoring Quadratics
To solve x² + 5x + 6 = 0: find two numbers that multiply to 6 and add to 5 → 2 and 3. Factor: (x+2)(x+3) = 0, so x = -2 or x = -3.
The Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a solves any quadratic. The discriminant b²−4ac tells how many real roots: positive = 2 roots, zero = 1 root, negative = no real roots.
Vertex Form
y = a(x−h)² + k. The vertex is at (h, k). Great for graphing and solving optimization problems — just read the vertex off directly.
Live Python Practice
Interactive Lab
Check Your Understanding
What does the discriminant b²−4ac tell you?
In y = a(x−h)² + k, the vertex is at:
To solve x² − 7x + 12 = 0 by factoring, you need two numbers that: