A quadratic equation is a collection of terms typically involving one letter, an equals sign, and some numbers. The letter represents an unknown, and you find its value when you solve an equation.
What is an example of an equation?
Simple linear equations are:
- x+3=5
- 2x-3=11
The solution to those are:
- x=2
- x=7
How do I solve quadratic equations?
A quadratic equation again involves a collection of numbers and letters with an equal sign. In addition, it will have a squared unknown term, which will be the novel’s highest power – what qualifies it as quadratic.
Examples of quadratic equations are:
- x^2+10x=-16
- 3y^2-4y+6=0
Quadratic equations are harder to solve than linear equations because making x the subject is trickier. We can solve quadratic equations by:
- factorizing
- using the quadratic formula
- completing the square
Quadratic equations typically offer two solutions, but some give only one, and others don’t.
What is the quadratic formula, and what is it used for?
The quadratic formula allows us to solve the general quadratic equation
By substituting into this formula:
The ± sign tells us to perform the calculation once with a plus and then with a minus; this typically gives two different answers for x.
For example, in the equation
Substituting into the quadratic formula gives
which simplifies to x = 5 or x = 2.
