AFOQT Practice Test

What is the standard form of a quadratic equation?

1. ax^2 + bx + c = 1

2. ax^2 + bx + c = 0

3. ax + b = c

4. ax^3 + bx^2 + c = 0

The correct answer is: ax^2 + bx + c = 0

The standard form of a quadratic equation is expressed as \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \). This format is crucial for identifying the coefficients of the quadratic expression. The \( ax^2 \) term is what makes the equation quadratic, as it indicates that the highest degree of \( x \) is 2. In the context of quadratic equations, it's common to set the equation equal to zero because this allows for the application of various methods for finding the roots of the equation, such as factoring, completing the square, or using the quadratic formula. The other options do not represent the standard form of a quadratic equation. For instance, setting it equal to 1 does not provide the necessary structure for analysis or solution methods. Similarly, a linear equation is represented by \( ax + b = c \) with a maximum power of 1, and the polynomial represented in the last option includes a cubic term, which moves beyond the definition of quadratic functions.