What Is a Quadratic Equation and How Can We Spot One?

A quadratic equation is a special kind of math equation.

It looks like this:

$$ax^2 + bx + c = 0$$

In this equation, the letters $a$, $b$, and $c$ are numbers (but $a$ can't be zero), and $x$ is the variable we are trying to solve for.

The important part of a quadratic equation is the $ax^2$ term. Because it has $x$ raised to the power of 2, we call it a second-degree polynomial.

How to Identify a Quadratic Equation

If you want to know if an equation is quadratic, look for these signs:

1. Look for $x^2$: Check if there is a term with $x$ raised to 2. If you find it, you probably have a quadratic equation.

2. Standard Form: See if you can rearrange the equation to look like $ax^2 + bx + c = 0$. The numbers $a$, $b$, and $c$ should be regular numbers, and $a$ can’t be zero.

3. No Higher Powers: Make sure there aren’t any terms with $x$ raised to a power greater than 2. For example, the equation $3x^3 + 2x + 1 = 0$ is not quadratic because of the $x^3$ part.

Examples of Quadratic Equations:

• The equation $2x^2 + 3x - 5 = 0$ is quadratic because it fits the form. Here, $a = 2$, $b = 3$, and $c = -5$.

• The equation $x^2 - 4 = 0$ is also quadratic. In this case, $a = 1$, $b = 0$, and $c = -4$.

Non-Examples:

• The equation $x^3 + 2x = 0$ is not quadratic because it has the $x^3$ term.

• The equation $y - 2 = 0$ isn’t quadratic either, because it does not have an $x^2$ term.

Understanding quadratic equations is important! You will find them often in math and in real life, like in science and money matters.