Identifying Quadratic Expressions
A quadratic expression is an algebraic expression of the second degree, which means it contains at least one term that is squared. The general form of a quadratic expression is \( ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero.
We can examine each option to determine which one is not a quadratic expression:
a) \( 3x^2 - x + 1 \): This is a quadratic expression with a leading term of degree 2 (\( 3x^2 \)).
b) \( x^3 -4 \): This is not a quadratic expression because it has a term with a power of 3 (\( x^3 \)), which makes it a cubic expression.
c) \( 4x^2 - 1 \): This is a quadratic expression with a leading term of degree 2 (\( 4x^2 \)).
d) \( 9 - x^2 \): This is a quadratic expression, though written with terms in reverse order, with the squared term having a degree of 2 (\( -x^2 \)).
So, the expression that is not a quadratic expression is option (b) \( x^3 -4 \).
