What is the vertex form of # f(x) = -3x^2 + 3x-2 #?
1 Answer
Dec 10, 2017
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"#