Notes for 11/3 BY JOVAN

Quadratic functions:

Ways to express quadratic function:

- f(x) = ax^2 + bx + c (General)

- c is y-intercept

- f(x) = a(x-h)^2 + k (Vertex form)

- coordinates of turning point (h, k)

- f(x) = a(x-p)(x-q) (Factor form)

- roots

- each form gives separate information about the graph

- General to Vertex - Completing the square

- General to Factor - Factorise

- Factor/Vertex to General - Expand

Ways to solve the equations:

- Using quadratic formula

- Completing the square

- Factorise

- Graph

- Sum and product of roots

- Calculator (DUH! =D)

Discriminant:

- b^2 - 4ac

- D > 0

- real and distinct roots (2 intersection on the x-axis)

- D = 0

- real and equal roots (1 intersection on the x-axis)

- D < 0

- imaginary/complex roots

Graphing (Sketching)

- roots, turning point, y-intercept

- shape: symmetrical

- smiley face-curve a > 0

- sad face-curve a < 0

- y-intercept: c

- Roots: solve