Understanding quadratic expressions is an important skill in Year 11 Math, especially when you start working with algebra. So, what exactly is a quadratic expression?

What Is a Quadratic Expression?

A quadratic expression usually looks like this:

$$ax^2 + bx + c$$

Here are some things to help you recognize a quadratic expression:

1. Degree: The highest power of the variable (which is $x$) is 2. For example, in the expression $3x^2 + 4x + 5$, the term $3x^2$ shows that the highest power is 2.

2. Coefficients: The numbers in front of $x^2$, $x$, and the constant (the $c$) can be any numbers. But the $a$ (the number in front of $x^2$) can’t be zero. For instance, in $2x^2 - 3x + 1$, we have $a=2$, $b=-3$, and $c=1$.

3. Shape: When you draw a graph of a quadratic expression, it makes a U-shaped curve called a parabola. It opens up if $a$ is positive (greater than 0) and opens down if $a$ is negative (less than 0).

Examples of Quadratic Expressions

Here are a couple of examples to clear things up:

• Example 1: The expression $x^2 + 2x + 1$ is quadratic because it can be written as $(x+1)^2$.

• Example 2: The expression $-4x^2 + 3$ is also quadratic. Here, $a=-4$, showing that $a$ can be negative and causes the parabola to open downwards.

Non-Quadratic Examples

Not all expressions are quadratic! For example, $5x^3 + 3x + 2$ is not quadratic because the highest power of $x$ is 3, not 2. Also, $7 + 2$ is just a number with no $x$ in it, so it's not a quadratic expression.

By learning these key features and patterns, spotting quadratic expressions will get easier as you move forward in your Year 11 Math studies!