Linear, Quadratic, and Exponential Models

A step-by-step guide to linear, quadratic, and exponential models

Functions are a type of mathematical relationship between inputs and outputs. The linear, quadratic, and exponential functions are the \(3\) main types of functions.

Linear function:

A linear function is a type of function whose highest exponent is \(1\). The standard form of this function is \(y=mx + b\). The graph of the linear function shows a straight line in the coordinate plane.

Quadratic function:

A quadratic function is a polynomial function with one or more variables, where the highest power of the variable is two. Since the highest degree in a quadratic function is of the second degree, it is also called the polynomial of degree \(2\).

The quadratic function, when graphed, makes parabolas. The standard form of a quadratic function is \(f(x) = ax^2+bx + c\), where \(a, b,\) and \(c\) are real numbers with \(a≠0\).

Exponential function:

An exponential function is a function of the form \(f(x)= a^x\), where \(x\) is a variable and \(a\) is a constant, which is called the base of the function and must be greater than \(0\). Exponential function graphs have curves. This curve can be vertical at first and then grow horizontally, or it can be horizontal at first and then become more vertical.