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

1 Answer
Jan 29, 2018

(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)