Definition
A quadratic expression is an expression of the form:
\[ ax^2 + bx + c \]
where:
- \( a, b, \) and \( c \) are real numbers (i.e., \( a, b, c \in \mathbb{R} \)),
- \( a \neq 0 \),
- \( x \) is the variable.
In this expression, \( ax^2 \) is the quadratic term, \( bx \) is the linear term, and \( c \) is the constant term.
Note
The requirement that \( a \neq 0 \) ensures that the expression is indeed quadratic, as the degree of the polynomial is two.
Examples of quadratic expressions:
-
\[ x^2 + 4x + 4 \]
-
\[ -2x^2 + 3x - 1 \]
-
\[ 3x^2 - 5x + 2 \]
-
\[ \frac{1}{2}x^2 - \frac{3}{4}x + \frac{5}{6} \]
-
\[ 5x^2 - 10 \]