When you start learning about quadratic equations in Year 12, it's easy to make mistakes that can cost you points. I've been there too, so I want to share some common mistakes and how to avoid them.

1. Forgetting the Quadratic Formula:
One big mistake is leaving out the quadratic formula. For equations like $ax^2 + bx + c = 0$, you can find solutions using:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

If you're not sure about this formula, practice it until it feels familiar!

2. Not Factoring Out:
Another common mistake is not factoring out any common numbers before using the quadratic formula or completing the square. If you see numbers that can be simplified, do it! For example, in $2x^2 + 4x = 0$, you can factor out a $2$ to get $2(x^2 + 2x) = 0$. This makes the math easier and helps you avoid mistakes.

3. Messing Up the Discriminant:
The discriminant, $b^2 - 4ac$, helps you understand the solutions. A lot of people make mistakes when calculating it. Be careful with the signs and don’t forget any negative signs. For example, if $b = -3$ and $a = 1$, make sure you calculate $(-3)^2 - 4(1)(c)$ correctly!

4. Ignoring Complex Solutions:
Sometimes, students are confused when they find complex solutions. If the discriminant is negative, the roots become complex, and that's okay! Don’t worry; if you get a negative number under the square root, write your solution like this: $x = a \pm bi$.

5. Rushing Through Steps:
When you're feeling the exam pressure, it's easy to rush and make simple mistakes. Always take a moment to check your work. Even a small mistake in multiplying can lead you to the wrong answer.

6. Misreading the Question:
Make sure you understand what the question is asking! Sometimes, it may ask for specific values of $x$, like in a word problem. If you focus too much on just solving, you might miss important details. Circle key phrases in the question to stay on track.

7. Not Trying Different Methods:
You can solve quadratics in different ways: by factoring, completing the square, or using the quadratic formula. If you only focus on one method, you might limit your understanding. Practice all three methods, as each might be better depending on the quadratic you’re working with.

By knowing these common errors and practicing regularly, you'll feel more confident in solving quadratic equations. Mastering these skills will not only help you in exams but will also boost your algebra skills for the future! Happy solving!