text: # Thread: maximum point of the curve
  
  1. ## maximum point of the curve
  
  The curve $y=-2x^2+8x-3$ has a maximum point at $x=p$,where $p$ is constant.Find the value of $p$
  
  2. Originally Posted by mastermin346
  The curve $y=-2x^2+8x-3$ has a maximum point at $x=p$,where $p$ is constant.Find the value of $p$
  A parabola opening downward has its maximum value at the vertex- and you can get that by completing the square:
  $-2x^2+ 8x- 3= -2(x^2- 4x)- 3= -2(x^2- 4x+ 4- 4)- 3$
  $= -2(x^2- 4x+ 4)+ 8- 3= -2(x- 2)^2+ 5$
  
  Since a square is never negative, that will be largest when x-2= 0.
explanation: The document contains a math question about finding the value of \( p \) where the curve \( y = -2x^2 + 8x - 3 \) has a maximum point. The document also includes a detailed answer that explains how to find the value of \( p \) by completing the square.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Thread: maximum point of the curve
  
  1. ## maximum point of the curve
  
  The curve $y=-2x^2+8x-3$ has a maximum point at $x=p$,where $p$ is constant.Find the value of $p$
  
  2. Originally Posted by mastermin346
  The curve $y=-2x^2+8x-3$ has a maximum point at $x=p$,where $p$ is constant.Find the value of $p$
  A parabola opening downward has its maximum value at the vertex- and you can get that by completing the square:
  $-2x^2+ 8x- 3= -2(x^2- 4x)- 3= -2(x^2- 4x+ 4- 4)- 3$
  $= -2(x^2- 4x+ 4)+ 8- 3= -2(x- 2)^2+ 5$
  
  Since a square is never negative, that will be largest when x-2= 0.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question about finding the value of \( p \) where the curve \( y = -2x^2 + 8x - 3 \) has a maximum point. The document also includes a detailed answer that explains how to find the value of \( p \) by completing the square.
  
  Label: question-and-answer