QUESTION 4
Given the quadratic number pattern:

Write down the value of the next term in the pattern.
Calculate an expression for the term of the quadratic pattern.
Determine the value of the SMALLEST term in this pattern.

The first part of this intriguing pattern shows that the terms are decreasing. If we observe closely, the difference between 69 and 0 is 69, and the difference between 0 and -63 is 63. Following this pattern, we can infer that the next term will decrease by an increasingly smaller amount, hinting that the next term should be around -63 minus a gradual decrease, which suggests the next term is -60.

For the second inquiry, we need to express the term. A general form for the term in a quadratic pattern is usually expressed as . By examining the terms and their differences, we can derive the coefficients – which leads to something like if we carefully formulate the pattern’s progression based on calculated differences.

One of the common mistakes when determining the smallest term is overlooking how a quadratic function behaves. It’s crucial to realize that the nature of quadratics means it will have a minimum or maximum point depending on the sign of the leading coefficient. Therefore, applying vertex concepts can help spot this smallest term more efficiently without missing vital details!