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
2x^2+ 5x + 3 = 0
In this one a = 2,b = 5 and c = 3
x^2− 3x = 0
This one is a little more tricky:
Where is a? Well a=1, as we don't usually write "1x^2"
b = − 3
And where is c? Well c = 0, so is not shown.
5x − 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!
x^2= 3x − 1
Move all terms to the left-hand side
x^2− 3x + 1 = 0
a = 1, b = −3, c = 1
2(w^2− 2w) = 5
Expand (undo thebrackets), and move 5 to left
2w^2− 4w − 5 = 0
a = 2, b = −4, c = −5
z(z−1) = 3
Expand, and move 3 to left
z^2− z − 3 = 0
a = 1, b = −1, c = −3
Look out for the next blog post on Solving Quadratic Equations