Algebra Practice Test: Prep & Practice Questions for Exam Readiness

A quadratic equation is defined as a polynomial equation of the second degree, which means it has the highest exponent of the variable \(x\) equal to 2. In the case of the equation presented, \(3x² - 2x + 1 = 0\), the term \(3x²\) clearly shows that the variable \(x\) is raised to the power of 2, fulfilling the criteria for a quadratic equation.

The other options do not meet this definition. The equation \(5x - 7 = 0\) is linear since the highest exponent of \(x\) is 1. Similarly, \(x + 4 = 0\) is also a linear equation for the same reason; it can be rearranged to \(x = -4\), showing it has only a single solution. Finally, the equation \(y = 2x + 3\) represents a linear function as well, as it can be rewritten in slope-intercept form and has a maximum exponent of 1 for the variable \(x\).

Therefore, the only equation among the choices that qualifies as quadratic is the one with the \(x²\) term.