### Functions: Quadratic functions

### Introduction

A **quadratic function** #f# is given by #f(x)=ax^2+bx+c# with #a#, #b# and #c# being real numbers and #a\neq 0#.

The graph associated with such a function is called a **parabola .**

When #a\gt0# then we speak of a **parabola opening upwards** and when #a\lt0# of a **parabola opening downwards**.

The significance of these names becomes evident from the graph below of the parabola opening upwards of #x^2-8# and the parabola opening downwards of #-x^2+8#.

To find the zeros of a quadratic function, we need to find the points of intersection of the parabola with the #x#-axis. We can do this in three ways:

- completing the square
- #abc#-formula
- factorization

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