identify the graph of $y = x^2$

the domain of $y = x^2$ is all real numbers. the range of $y = x^2$ is
all real numbers
$y 0$
$y \ge 0$

Question

identify the graph of $y = x^2$

the domain of $y = x^2$ is all real numbers. the range of $y = x^2$ is
all real numbers
$y > 0$
$y \ge 0$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Quadratic Parent Function", "Domain and Range of Quadratic Functions" ], "new_concepts": [], "current_concepts": [ "Quadratic Parent Function", "Domain and Range of Quadratic Functions" ] } ## Identify the correct graph Using the *Quadratic Parent Function* knowledge point $$ \begin{aligned} &y = x^2\ &\text{Vertex: } (0,0)\ &\text{Points: } (1,1), (-1,1), (2,4), (-2,4)\ &\text{Orientation: Opens upward} \end{aligned} $$ ## Determine the domain Using the *Domain and Range of Quadratic Functions* knowledge point $$ \begin{aligned} &\text{Domain: } x \in \mathbb{R}\ &\text{Domain selection: all real numbers} \end{aligned} $$ ## Determine the range Using the *Domain and Range of Quadratic Functions* knowledge point $$ \begin{aligned} &\text{Since } x^2 \ge 0 \text{ for all real } x:\ &y \ge 0\ &\text{Range selection: } y \ge 0 \end{aligned} $$ Identify the graph of $y = x^2$: The third graph (opening upward with vertex at $(0,0)$). The domain of $y = x^2$ is all real numbers. The range of $y = x^2$ is $y \ge 0$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Domain and Range of Quadratic Functions" ] }

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Question

Explanation:

Identify the correct graph

Determine the domain

Determine the range

Answer: