some points on the curve $y = -x^2 + 5$ have been plotted.

which of the points a-f shows where the point at $x = 3$ should be plotted?

Question

some points on the curve $y = -x^2 + 5$ have been plotted.

which of the points a-f shows where the point at $x = 3$ should be plotted?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Quadratic Evaluation", "Table of Values" ], "new_concepts": [ "Graphing Quadratic Functions" ], "current_concepts": [ "Quadratic Evaluation", "Table of Values", "Graphing Quadratic Functions" ] } ## Evaluate the quadratic equation at $x = 3$ $$ y = -x^2 + 5 $$ $$ y = -(3)^2 + 5 = -9 + 5 = -4 $$ ## Identify the corresponding point on the graph The coordinates of the point are $(3, -4)$. ## Match the coordinates with the plotted points Looking at the vertical line $x = 3$: - Point A is at $(3, 14)$ - Point B is at $(3, 4)$ - Point C is at $(3, 1)$ - Point D is at $(3, 0)$ - Point E is at $(3, -4)$ - Point F is at $(3, -14)$ Therefore, point E represents the correct location.

(A) A

(B) B

(C) C

(D) D

(E) E

(F) F

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QUESTION IMAGE

Question

Explanation:

Evaluate the quadratic equation at \(x = 3\)

Identify the corresponding point on the graph

Match the coordinates with the plotted points

Answer: