Understanding the standard form of a quadratic equation isn’t too hard! A quadratic equation usually looks like this:

$ax^2 + bx + c = 0$

Here’s what those symbols mean:

• $a$ is the number in front of the $x^2$ term. This is called the quadratic term, and it can’t be zero.
• $b$ is the number in front of the $x$ term. We call this the linear term.
• $c$ is just a constant number without any $x$.

To check if you have a quadratic equation, look for that $x^2$ term. If it’s there, awesome! You’re working with a quadratic.

Here’s a simple checklist to help you identify the standard form:

1. Find the highest power of $x$.

   • If the highest power is 2 (because of the $x^2$ term), then you have a quadratic!

2. Look at the order of the terms.

   • The equation should start with the $x^2$ term, then the $x$ term, and finally the constant. It should look like this: $ax^2 + bx + c = 0$.

3. Spot the coefficients.

   • Make sure you can identify $a$, $b$, and $c$. For example, in the equation $3x^2 + 4x - 5 = 0$:
     • Here, $a = 3$, $b = 4$, and $c = -5$.

4. Be careful with rearrangements!

   • Sometimes, the equation might not be in the standard form, like $4x - 3x^2 = 5$. You can rearrange it to $-3x^2 + 4x - 5 = 0$ and easily spot $a$, $b$, and $c$. Just make sure the $x^2$ term stays positive. If it’s negative, you can multiply everything by -1 to fix it.

Once you understand this formula, solving and graphing quadratic equations will be much easier! Plus, this skill will help you with tougher problems later on. Just remember, with a bit of practice, spotting these equations will become super easy!