Question

What is the vertex of `y= 2(x-5)^2-x^2-3x-1`?

Answer 1

`(23/2,-333/4)`

Explanation:

`"require to express y in standard form"`

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

`rArry=2(x^2-10x+25)-x^2-3x-1`

`color(white)(rArry)=2x^2-20x+50-x^2-3x-1`

`color(white)(rArry)=x^2-23x+49larrcolor(blue)"in standard form"`

`"with "a=1,b=-23" and "c=49`

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

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

`rArrx_(color(red)"vertex")=-(-23)/2=23/2`

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

`y_(color(red)"vertex")=(23/2)^2-23(23/2)+49`

`color(white)(xxxx)=529/4-529/2+49=-333/4`

`rArrcolor(magenta)"vertex "=(23/2,-333/4)`