Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

When is a function considered quadratic?

1. When it has two distinct variables

2. When it can be expressed as an equation of the form y = mx + b

3. When it includes a variable raised to the second power

4. When its graph is a horizontal line

The correct answer is: When it includes a variable raised to the second power

A function is considered quadratic when it includes a variable raised to the second power. This characteristic defines a quadratic function, typically expressed in the standard form as \( y = ax^2 + bx + c \), 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 function its parabolic shape when graphed, differentiating it from linear functions, which only involve the first power of the variable. In contrast, options representing alternative characteristics do not define a quadratic function. A function with two distinct variables pertains to multivariable functions, not specifically quadratic ones. Equations of the form \( y = mx + b \) describe linear functions, which are the first degree in \( x \), rather than quadratic. Lastly, a horizontal line represents a constant function, which does not involve any variable raised to a power, thus failing to meet the criteria for being quadratic. Hence, the correct understanding of a quadratic function centers on the presence of a squared term.