What is #y = x^2-16x+40# written in vertex form?

1 Answer
Jim G.
Mar 26, 2018

#y=(x-8)^2-24#

Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a is"#
#"a multiplier"#

#"Give the equation in "color(blue)"standard form"#

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

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

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

#y=x^2-16x+40" is in standard form"#

#"with "a=1,b=-16" and "c=40#

#rArrx_(color(red)"vertex")=-(-16)/2=8#

#"substitute "x=8" into the equation for y-coordinate"#

#y_(color(red)"vertex")=8^2-(16xx8)+40=-24#

#rArr(h,k)=(8,-24)#

#rArry=(x-8)^2-24larrcolor(red)"in vertex form"#

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