allie claims that this data represents a quadratic relation. is she correct?

yes
no

Question

allie claims that this data represents a quadratic relation. is she correct?

yes
no

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "First Differences" ], "new_concepts": [ "Second Differences", "Quadratic Relations" ], "current_concepts": [ "First Differences", "Second Differences", "Quadratic Relations" ] } ## Calculate first differences Using the *First Differences* knowledge point $$ \begin{aligned} \Delta y_1 &= 88.75 - 90 = -1.25 \ \Delta y_2 &= 85 - 88.75 = -3.75 \ \Delta y_3 &= 78.75 - 85 = -6.25 \ \Delta y_4 &= 70 - 78.75 = -8.75 \ \Delta y_5 &= 58.75 - 70 = -11.25 \ \Delta y_6 &= 45 - 58.75 = -13.75 \end{aligned} $$ ## Calculate second differences Find differences of consecutive first differences. $$ \begin{aligned} \Delta^2 y_1 &= -3.75 - (-1.25) = -2.5 \ \Delta^2 y_2 &= -6.25 - (-3.75) = -2.5 \ \Delta^2 y_3 &= -8.75 - (-6.25) = -2.5 \ \Delta^2 y_4 &= -11.25 - (-8.75) = -2.5 \ \Delta^2 y_5 &= -13.75 - (-11.25) = -2.5 \end{aligned} $$ ## Determine relation type Constant second differences indicate quadratic. Since second differences are constant, Allie is correct.

yes

no

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Relations" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate first differences

Calculate second differences

Determine relation type

Answer: