An equation is considered quadratic if it can be expressed in the standard form: ax² + bx + c = 0, where:
- a, b, and c are constants
- a is not equal to zero (if a = 0, it becomes a linear equation)
Quadratic equations are characterized by the presence of the variable x raised to the power of 2 (thus the term x²). To determine if a given equation is quadratic, follow these steps:
- Rearrange the equation so one side is equal to zero.
- Check if the highest power of the variable is 2.
- Ensure that the coefficient of x² (the a value) is not zero.
If all these conditions are satisfied, you have a quadratic equation. For example, the equation 2x² – 3x + 5 = 0 is quadratic since it fits the form and has a = 2, b = -3, and c = 5.