What is the vertex form of # f(x) = -3x^2 + 3x-2 #?

1 Answer
Dec 10, 2017

#f(x)=-3(x-1/2)^2-5/4#

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"#

#"given the parabola in "color(blue)"standard form"#

#f(x)=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)#

#f(x)=-3x^2+3x-2" is in standard form"#

#"with "a=-3,b=3" and "c=-2#

#rArrx_(color(red)"vertex")=-3/(-6)=1/2#

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

#y_(color(red)"vertex")=-3(1/2)^2+3(1/2)-2=-5/4#

#rArrf(x)=-3(x-1/2)^2-5/4larrcolor(red)"in vertex form"#