I don't understand what this question is asking me to do if someone could explain that would be greatly appreciated!! Find the maximum value for the following quadratic equation...?

f(x) = x -­ 2x2 ­ - 1

1 Answer
Jim G.
Jan 26, 2018

#"maximum value "=-7/8#

Explanation:

#"to determine the maximum/minimum value we"#
#"require the coordinates of the vertex"#

#"given a quadratic equation in "color(blue)"standard form"#

#•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0#

#"then the x-coordinate of the vertex is"#

#x_(color(red)"vertex")=-b/(2a)#

#"rearrange "y=x-2x^2-1" into standard form"#

#rArry=-2x^2+x-1larrcolor(blue)"in standard form"#

#"with "a=-2,b=1" and "c=-1#

#rArrx_(color(red)"vertex")=-1/(-4)=1/4#

#"substitute this value into the equation for y"#

#y_(color(red)"vertex")=-2(1/4)^2+1/4-1#

#color(white)(xxxxxxxxxx)=-1/8+2/8-8/8=-7/8#

#rArrcolor(magenta)"vertex "=(1/4,-7/8)#

#"to determine maximum/minimum consider the sign"#
#"of a the coefficient of the "x^2" term"#

#• " if "a>0" then y is a minimum"#

#• "if "a<0" then y is a maximum"#

#"here "a=-2<0" hence y is a maximum"#

#rArr"maximum value is "y=-7/8#
graph{-2x^2+x-1 [-10, 10, -5, 5]}

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