Let’s begin with the basic terminology.
“If I had a dollar for every time Algebra has helped me, I’d have x dollars”.
Algebra: Basic Operations
Just like how we can use operations on numbers, we can add, subtract, multiply, and divide variables as well.
Solving Algebraic Equations
We can now start to solve equations with the rules we’ve just learnt. The point of these equations is to find the value of the variable.
Introduction to the Quadratic
The next step of our journey into the world of algebra is the quadratic, which is something you’ll see over and over in your high school maths classes. A quadratic is an expression which contains an x2 squared term with no higher powers.
All quadratics have the following form, where a and b are both coefficients, and c is a constant.
Some Examples of Alegbra
Not all quadratics look the same. The only real identifier of a quadratic is that the highest power of x is 2.
To reverse this process is called factorising. Let’s consider the example to the left, 3 x2 + 5 x + 2.
1) Multiply the a coefficient by the constant c (in our case 3×2)
2) Find two numbers which add to the b coefficient (5) and multiply to our product ac (6). In our case, this would be 3 and 2.
3) Split the b term up into a sum containing these two
4) Take out any common terms that appear. In our case, the first two terms both contain a 3x and the second two terms both contain a 2.
5) Join these two terms as shown to give a factorised form.
Not all quadratics can be factorised!
Sometimes you’ll come across a quadratic that no matter how hard you try, you can’t seem to factorise it. Don’t stress, it’s probably because it can’t be done!
Solving Quadratic Equations
Now that we know what a quadratic is and how to factorise, we can start to solve them.
Sometimes it can be difficult to factorise a quadratic in order to solve it. In this case, we use the trusty quadratic formula.
Now don’t start to panic, the quadratic formula may seem daunting, but it will become your best friend in years to come!
The solutions to any quadratic will be given by substituting in the coefficients a, b, and the constant c into this formula
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