Lesson Summary

When studying quadratic functions such as parabolas and their behaviour, it becomes evident that they do not exhibit the linear growth seen in straight lines. Here's a breakdown of the rate of change observed in a parabola: for each unit of increment of the x variable, there is a different value for its y increment.

While in a linear equation, the first differences between corresponding y-values are constant, reflecting a linear growth pattern, this is not the case for quadratics, where the growth rates differ. By computing the first differences in the y-values of a parabola, these numbers (7, 5, 3, 1) are derived.

By manipulating these first differences, we can also determine what are known as second differences. Subsequently, subtracting the first differences (e.g., 7 - 5) from each other can provide additional insight into the growth patterns of the quadratic function.