# Identifying Quadratic Equation

This post aims to equip students with the knowledge of how to identify whether an equation is indeed a quadratic equation. Identifying the equation is crucial in solving an equation. After identifying, students can then proceed to the various method towards solving an equation, which will be covered in other posts.

An example of a Quadratic Equation:

Quadratic Equations make nice curves, like this one:

The name **Quadratic **comes from "quad" meaning square, because of the variable gets squared (like **x^2**).

It is also called an "Equation of Degree 2" (because of the "2" on the **x**)

The **Standard Form **of a Quadratic Equation looks like this:

**a**, **b** and **c** are known values. **a** can't be 0.

"**x**" is the **variable** or unknown (we don't know it yet).

**Here are some examples**

__Example 1__

**2x^2+ 5x + 3 = 0**

In this one **a = 2**,**b = 5 **and **c = 3**

__Example 2__

**x^2âˆ’ 3x = 0**

This one is a little more tricky:

Where is **a**? Well **a=1**, as we don't usually write "1x^2"

**b = âˆ’ 3**

And where is **c**? Well **c = 0**, so is not shown.

__Example 3__

**5x âˆ’ 3 = 0**

(in other words, s **not **a quadratic equation: it is missing **x^2**

(in other words **a = 0**, which means it can't be quadratic)

**Hidden Quadratic Equations**

As we saw before, the **Standard Form** of a Quadratic Equation is

ax^2+ bx + c = 0

But sometimes a quadratic equation doesn't look like that!

__For example__

__Example 1__

**x^2= 3x âˆ’ 1**

Move all terms to the left-hand side

**x^2âˆ’ 3x + 1 = 0**

a = 1, b = âˆ’3, c = 1

__Example 2__

**2(w^2âˆ’ 2w) = 5**

Expand (undo thebrackets), and move 5 to left

**2w^2âˆ’ 4w âˆ’ 5 = 0**

a = 2, b = âˆ’4, c = âˆ’5

__Example 3__

**z(zâˆ’1) = 3**

Expand, and move 3 to left

**z^2âˆ’ z âˆ’ 3 = 0**

a = 1, b = âˆ’1, c = âˆ’3

Look out for the next blog post on **Solving Quadratic Equations**