# Linear, Quadratic, and Exponential Models

Functions are a type of mathematical relationship between inputs and outputs. In this guide, you will learn more about types of functions.

**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, therefore 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 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.

## Related to This Article

### More math articles

- How to Solve One-Step Equations? (+FREE Worksheet!)
- Quadrilaterals and Rectangles
- How to Understand the Key Properties of Trapezoids
- Measurements – Time
- The Ultimate 7th Grade AZMerit Math Course (+FREE Worksheets)
- FREE 5th Grade Common Core Math Practice Test
- Identify Lines of Symmetry
- Top 10 8th Grade Common Core Math Practice Questions
- PSAT Math Formulas
- How to Master Polynomial Functions

## What people say about "Linear, Quadratic, and Exponential Models - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.