#"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"#
#•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)#
#7y=4x^2+2x-3larrcolor(blue)"divide all terms by 7"#
#rArry=4/7x^2+2/7x-3/7larrcolor(blue)"in standard form"#
#"with "a=4/7,b=2/7#
#rArrx_(color(red)"vertex")=-(2/7)/(8/7)=-1/4#
#"substitute this value into equation for y-coordinate"#
#y_(color(red)"vertex")=4/7(-1/4)^2+2/7(-1/4)-3/7#
#color(white)(xxxx)=1/28-2/28-12/28=-13/28#
#"here "a=4/7" and "(h,k)=(1/4,-13/28)#
#rArry=4/7(x+1/4)^2-13/28larrcolor(red)"in vertex form"#
