What is the vertex form of #y=-5/8x^2+7/4x +2/3#?
1 Answer
Feb 8, 2018
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 equation in 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=-5/8x^2+7/4x+2/3" is in standard form"#
#"with "a=-5/8,b=7/4" and "c=2/3#
#rArrx_(color(red)"vertex")=-(7/4)/(-5/4)=7/5#
#"substitute this value into the equation for y"#
#y_(color(red)"vertex")=-5/8(7/5)^2+7/4(7/5)+2/3=227/120#
#rArry=-5/8(x-7/5)^2+227/120larrcolor(blue)"in vertex form"#
