What is the vertex of # y= 2(x-5)^2-x^2-3x-1#?
1 Answer
Jan 29, 2018
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)#
