Quadratic Equation
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A quadratic equation is an equation of the second degree (its highest exponent is 2) with a standard form that can be written:
ax^2 + bx + c = 0
where a, b, and c are constants, and a does not equal 0 (if a = 0), the equation is not quadratic, but linear). The variable x is raised to the second power, which is why it's called a quadratic equation.
Key characteristics of quadratic equations:
Degree: The highest exponent of x is 2.
Standard form: The equation is typically written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers, and a does not equal 0.
Solutions: Quadratic equations can have two, one or zero solutions, which may be real or complex, depending on the discriminant (b^2 - 4ac).
Example:
The equation 2x^2 + 3x - 5 = 0 is a quadratic equation, where:
a = 2
b = 3
c = -5
Quadratic equations can be solved using methods like factoring, completing the square, or using the quadratic formula.