The quadratic term in a quadratic equation is easily identified; it's the term containing the variable raised to the power of 2.
Understanding Quadratic Equations
A quadratic equation is an equation of the form: ax² + bx + c = 0, where:
- 'a', 'b', and 'c' are constants.
- 'a' is not equal to zero (a ≠ 0). This is crucial because if 'a' were zero, the equation wouldn't be quadratic; it would be linear.
- 'x' is the variable.
The term ax² is the quadratic term. The term bx is the linear term, and c is the constant term.
Identifying the Quadratic Term
To find the quadratic term, simply look for the term in the equation where the variable (usually 'x') is squared (raised to the power of 2). The coefficient of this term (the number multiplied by x²) is 'a'.
Examples:
- 3x² + 5x - 2 = 0: The quadratic term is 3x².
- -x² + 7x + 10 = 0: The quadratic term is -x² (where 'a' = -1).
- x² - 9 = 0: The quadratic term is x² (where 'a' = 1).
As noted in the provided reference materials, a quadratic function is of the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. The term ax² is explicitly identified as the quadratic term. This aligns perfectly with our understanding of quadratic equations. Whether it is a function or an equation, the identification of the quadratic term remains the same.
Various online resources (like the Dartmouth OpenCalc2 lecture notes) further solidify this understanding.
