Any equation, whether it be linear, quadratic, exponential or some other type of equation, is asking you to solve for the variable
in the equation. A quadratic equation
written in standard form
is an equation
that can be solved for x. Solving will give you at most two values for x.
There are a variety of techniques for solving quadratic equations. This lesson will focus on what it means to solve a quadratic equation. To see details about specific methods for solving, click one of the links below:
Solving by Factoring
Solving by Using the Quadratic Formula
The standard form of a quadratic equation,
, is called the standard form because we will always need to get our equations to look like this before solving. If an equation
is not in standard form, we must manipulate it until it is. If you link to the lessons on solving by factoring or solving by using the quadratic formula, you will see that we must always begin with the standard form.
When graphing a quadratic function, it is usually presented as
which is very similar to the standard form of a quadratic equation. The y has simply been replaced with a 0. Whenever we set y = 0 in any function, we are finding the x–intercept(s) for that function. So when we solve a quadratic in the form
we are really finding the x–intercepts. These x–intercepts are also called roots. Another term for roots or x-intercepts is zeros.
So, when we solve a quadratic in the form
we are finding the roots of the function.
There are a lot of terms used simultaneously and interchangeably when working with quadratics and many students get confused about what they are trying to do. The following examples should clarify what is being done when solving quadratic equations.