What characterizes a quadratic equation?

• A. It has the form y = mx + b
• B. It contains a term raised to the second power
• C. It cannot be graphed
• D. It only contains linear terms

Answer: (B)

A quadratic equation is characterized by containing a term raised to the second power, which distinguishes it from linear equations. Specifically, the standard form of a quadratic equation is expressed as ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants and ( a ) is not equal to zero. The presence of the ( x^2 ) term is what gives the equation its quadratic nature, allowing it to represent a parabolic graph.

Quadratic equations can be graphed, yielding a U-shaped curve (the parabola), which highlights that they have distinct characteristics such as symmetry and vertex, unlike linear equations that graph as straight lines. Thus, the defining trait of a quadratic equation is indeed the presence of the squared term, reinforcing that this option accurately identifies the essence of what makes an equation quadratic.