Question

What is the vertex of `y= -2x^2+x-(x-3)^2`?

Answer 1

`"vertex "=(7/6,-59/12)`

Explanation:

`"expand and simplify into "color(blue)"standard form"`

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

`y=-2x^2+x-(x^2-6x+9)`

`color(white)(y)=-2x^2+x-x^2+6x-9`

`color(white)(y)=-3x^2+7x-9`

`"with "a=-3,b=7" and "c=9`

`"given the quadratic in standard form the x-coordinate"`
`"of the vertex is"`

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

`rArrx_(color(red)"vertex")=-7/(-6)=7/6`

`"substitute "x=7/6" into the equation for y"`

`y_(color(red)"vertex")=-3(7/6)^2+7(7/6)-9=-59/12`

`rArrcolor(magenta)"vertex "=(7/6,-59/12)`