A quadratic equation is an equation
in the form:
x is a variable. It is an unknown.
a, b and c are constants, where a cannot equal 0. They stand in for numbers.
The Oxford English Dictionary defines a quadratic equation as "an equation of the second degree; specifically an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and x is unknown."
Understanding Quadratic Equations
It is easier to understand quadratic examples with an example. Let's look at a quadratic equation.
This is the quadratic equation shown at the start of the lesson with a
= 2, b
= 3 and c
This a quadratic
equation because of the x2
A quadratic equation is an equation where the highest power
What Quadratic Equations Are...
Here are some real examples of quadratic equations.
They are all in the standard form ax2 + bx + c = 0
|3x2 + 5x + 2 = 0
||a = 3, b = 5, c = 2
|x2 + 4x + 3 = 0
||a = 1, b = 4, c = 3 (no need to write 1x2)
|x2 − 4x + 4 = 0
||a = 1, b = −4, c = 4
The following equations are also quadratic equations, but they are not in standard form:
|x2 = 2 − 5x
||This looks different because some terms have been moved to the other side of the equals sign.
|4x2 + 1 = 0
||There is no x term (so b = 0), but the highest power of x is still 2.
|2(x2 − x) = 3
||The left hand side is factored and another term has been moved to the other side of the equals sign.
|x(x + 2) = 0
||When the bracket is expanded, you get a x2 term.
...And What Quadratic Equations Aren't
These equations are not
|x + 2 = 0
||There is no x2 term (a = 0). This is a linear equation.
|x3 + 2x2 + 3x + 4 = 0
||There is a x3 term. The highest power of x is 3, not 2. This is a cubic equation.
The Graph of a Quadratic Equation
A quadratic equation can be plotted on a graph.
Plot the function:
The graph of a quadratic equation looks like a curve:
What's in a Name?
The word "quadratic" comes from the word "quad", meaning "square" - because the x