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.