A quadratic expression is an expression that has the highest power of the variable being a power of two and it must have a power of two in the expression
Since the variable is x, it must have an x^2 and cannot have any expression higher
5x^2 + 9x - 1 is a quadratic expression
9x-2 does not have a x^2 term
x-12x³+8x²-7x+1 has a term to the third power which makes it a cubic expression