Section 2.1: Quadratic Functions

Polynomial functions are classified by degree.

• Constant Function- f(x) = a, a ≠0. This polynomial function has a degree of 0.
  

Example: f(x)=2

• Linear Function- f(x) = mx + b, m≠0. This polynomial function has a degree of 1. The slope of this function is m and y-intercept is (0,b).

• Example: f(x) = x
• Quadratic Function: f(x) = ax² + bx + c. Let a, b, and c be real numbers with a ≠0.

Example: f(x) = x²

• Standard form of a Quadratic Function: f(x) = a(x-h)² + k, a ≠0 where the vertex is ( h, k)

Example: Write a quadratic function in standard form by completing the square.

f(x) = 2x² + 8x + 7
f(x) = 2(x² + 4x) + 7
f(x) = 2(x² + 4x + 4) + 7
f(x) = 2(x² + 4x + 4) - 2(4) + 7
f(x) = 2(x + 2)² -1

• Maximum and Minimum- if a>0, f has a minimum that occurs at
  x = -b/2a.

If a<0, f has a maximum that occurs at x= -b/2a.