Quadratic Polynomials

Quadratic Polynomials and Functions (Definition)

We assume that you are familiar with expanding the product of two linear functions:

(x + a)(x + b)

A quadratic polynomial in x is an expression of the form ax² + bx+ c, where a 0.

Here are some examples:

x² − x − 2

x² − 1

2x² + x + 1

(x − 2)(x − 3) = x² − 5x + 6

A quadratic function is a function of the form y = ax² + bx+ c, where a 0.

We first look at functions of the form y = ax².
Since x² ≥ 0 for any x, the value of y = ax² has the same sign as a.

Note that at each x-value, the magnitude of y = ax² grows as the magnitude of a grows.