Exercise os A quadratic pattern has a second term A third term equal to -6 and a sth te equal to -14 - Calculate the second difference of this quadratic pattern (5)

To find the second difference of a quadratic pattern, we begin by identifying the coefficients of the quadratic equation, usually expressed in the form \( a_n = an^2 + bn + c \). Given that the third term is -6 (when n=3) and the fifth term is -14 (when n=5), we can set up equations based on this information. Once we have the first differences from the terms, we calculate the second differences, which remain constant for quadratic patterns. The constant value is what you're looking for when calculating the second difference. An engaging trick to remember: imagine your quadratic function like a roller coaster—every bump and rise represents a change in the y-value as you move along the x-axis. The first difference signifies the initial excitement (or decline) in elevation between the seats on the ride, while the second difference tells you if that ride is leveling out or getting wilder!