choose the function which has maximum value.

$ y = x^2 + 3x + 2 $

$ y = -5x^2 + x + 2 $

Question

choose the function which has maximum value.

$ y = x^2 + 3x + 2 $

$ y = -5x^2 + x + 2 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Maximum of Quadratic Function", "Direction of Parabola Opening" ], "current_concepts": [ "Quadratic Equations", "Vertex of Quadratic Function", "Maximum of Quadratic Function", "Direction of Parabola Opening" ] } ## Analyze the direction of opening for the first function $$ \begin{aligned} &y = x^2 + 3x + 2 \ &a = 1 > 0 \implies \text{Opens upward} \implies \text{Has a minimum value} \end{aligned} $$ ## Analyze the direction of opening for the second function $$ \begin{aligned} &y = -5x^2 + x + 2 \ &a = -5 < 0 \implies \text{Opens downward} \implies \text{Has a maximum value} \end{aligned} $$

(A) $y = x^2 + 3x + 2$

(B) $y = -5x^2 + x + 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of Quadratic Function" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Analyze the direction of opening for the first function

Analyze the direction of opening for the second function

Answer: