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

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

- 1
- 4
- 2

Question

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

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

- 1
- 4
- 2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "First Differences", "Second Differences", "Quadratic Relations" ], "new_concepts": [], "current_concepts": [ "First Differences", "Second Differences", "Quadratic Relations" ] } ## Calculate the first differences $$ \begin{aligned} \Delta y_1 &= 11 - 5 = 6 \ \Delta y_2 &= 19 - 11 = 8 \ \Delta y_3 &= 29 - 19 = 10 \end{aligned} $$ ## Calculate the second differences $$ \begin{aligned} \Delta^2 y_1 &= 8 - 6 = 2 \ \Delta^2 y_2 &= 10 - 8 = 2 \end{aligned} $$

1

4

2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Second Differences" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the first differences

Calculate the second differences

Answer: