Question

11. Describe the difference between a linear and quadratic relation. Consider these points to assist you in developing your response)
• Equation
• First and second differences
• Graph

Answer 1

A linear relation is one where the equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The first differences between consecutive y-values are constant, whereas the second differences are zero. The graph of a linear relation is a straight line.

A quadratic relation is one where the equation is of the form y = ax^2 + bx + c, where a, b, and c are constants. The first differences between consecutive y-values are not constant, but the second differences are constant. The graph of a quadratic relation is a parabola.

In other words, a linear relationship shows a constant change in y for every change in x, while a quadratic relationship shows an increasing or decreasing change in y as x increases or decreases. A linear relationship has a constant slope, while a quadratic relationship has a changing slope. The two types of relationships can be easily distinguished by examining the first and second differences in the y-values and by looking at the shape of their corresponding graphs.