Question

What is the vertex of `y= -(x+1)^2+2x^2-x`?

Answer 1

`(3/2,-13/4)`

Explanation:

`"expand and simplify right side of the equation "`

`y=-(x^2+2x+1)+2x^2-x`

`color(white)(y)=-x^2-2x-1+2x^2-x`

`color(white)(x)=x^2-3x-1larrcolor(blue)"in standard form"`

`"with "a=1,b=-3" and "c=-1`

`"the x-coordinate of the vertex is "`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)=-(-3)/3=3/2`

`"substitute this value into equation for y-coordinate"`

`y_(color(red)"vertex")=(3/2)^2-3(3/2)-1=-13/4`

`rArrcolor(magenta)"vertex"=(3/2,-13/4)`