Question

what are the first differences for the terms of the quadratic equation \\(y = x^2 + 3x + 1\\), for \\(x = \\{1, 2, 3, 4\\}\\)?

\\(\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 1 & 5 \\\\ \\hline 2 & 11 \\\\ \\hline 3 & 19 \\\\ \\hline 4 & 29 \\\\ \\hline \\end{array}$$

\\)

• 19, 29, 41
• 8, 10, 12
• 11, 19, 29
• 6, 8, 10

Explanation:

Identify the given sequence of y-values

$$ y = [5, 11, 19, 29] $$

Calculate successive differences between consecutive terms

$$
LATEXBLOCK0
$$

Match the calculated differences with the options

$$ \text{First differences} = 6, 8, 10 $$

Answer:

• 19,29,41
• 8,10,12
• 11,19,29
• 6,8,10 (Correct answer)