Quadratic Equations

What is a quadratic equation?

A quadratic equation is a polynomial of degree two. Its general form is \[ax^2+bx+c=0\] where \(a\neq0\). It can be solved to find \(x\) in 3 main ways:

Click on one of the above links to find out more and see worked examples.

A solution of a quadratic equation is often also called a "root". Click here to find out about how the discriminant can be used to find out how many roots any given equation has.

What is a root of an equation?

For a given quadratic equation \[y=ax^2+bx+c\] we can sketch the graph. Take the equation \[y=x^2-1\] The graph looks like the one shown here:
Graph of f(x)=x^2-1
A root is found when \(y=0\). With \(y\) being the vertical axis, this simply means "when the graph intersects the \(x\) axis". The roots are highlighted in this image, you may notice that the \(y\) coordinate is \(0\) in both, by the definition of a root. The \(x\) coordinates are found through one of the above 3 methods.
Graph of f(x)=x^2-1 with roots