Which expression represents the quadratic equation in standard form?

To determine which expression represents a quadratic equation in standard form, it's essential to understand what standard form for a quadratic equation is. A quadratic equation is typically expressed as ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants, and ( a ) must be non-zero.

The expression that correctly fits this definition is ( 2x^2 + 3x + 1 = 0 ). In this expression:

• The term ( 2x^2 ) represents the quadratic term, where ( a = 2 ).

• The term ( 3x ) represents the linear term, where ( b = 3 ).

• The constant term ( 1 ) represents ( c ).

Thus, it clearly conforms to the required structure of a quadratic equation in standard form.

In contrast, the other expressions do not fit the standard form of a quadratic equation. For instance, the expression ( x^2 + 5 = 0 ) is a quadratic equation but lacks a linear term. The expression ( 3x - 2 = 0 ) is linear, not quadratic, and therefore does not contain an (