what are the solution(s) of $-x^2 + 2x + 3 = x^2 - 2x + 3$?

-1 and 3
0 and 2
1
3

Question

what are the solution(s) of $-x^2 + 2x + 3 = x^2 - 2x + 3$?

-1 and 3
0 and 2
1
3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Intersection of Quadratic Graphs" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Intersection of Quadratic Graphs" ] } ## Equate the functions and simplify $$ \begin{aligned} -x^2 + 2x + 3 &= x^2 - 2x + 3 \ -2x^2 + 4x &= 0 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} -2x(x - 2) &= 0 \ x = 0 \quad &\text{or} \quad x = 2 \end{aligned} $$ ## Verify with the graph The intersection points of the two parabolas $y = -x^2 + 2x + 3$ and $y = x^2 - 2x + 3$ occur at $(0, 3)$ and $(2, 3)$, which correspond to the $x$-values: $$ x = 0, \quad x = 2 $$

-1 and 3

0 and 2

1

3

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

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QUESTION IMAGE

Question

Explanation:

Equate the functions and simplify

Solve the quadratic equation

Verify with the graph

Answer: