# maximum point of the curve

• Jul 21st 2010, 11:40 PM
mastermin346
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 $p$
• Jul 22nd 2010, 12:10 AM
HallsofIvy
Quote:

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.