AFOQT Practice Test

What is the general structure of a quadratic equation?

1. ax² + bx + c = 0

2. ax + b = c

3. ax³ + bx + c = 0

4. ax² + bx = 0

The correct answer is: ax² + bx + c = 0

The general structure of a quadratic equation is represented by the equation ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients and 'x' is the variable. This specific form is crucial because it characterizes a polynomial of degree 2, which means it can graphically represent a parabola when plotted. The coefficient 'a' must be non-zero for it to qualify as a quadratic equation, as its absence would reduce the equation to a linear form instead. The terms in the equation have distinct roles: 'ax²' represents the quadratic term, 'bx' is the linear term, and 'c' is the constant term. This structure allows for methods such as factoring, completing the square, and applying the quadratic formula, which provides solutions for 'x'. In contrast, the other choices either depict equations of different degrees (like linear or cubic) or lack a constant term, further distinguishing them from the standard quadratic format.