What is the vertex form of #y=-3x^2-x+9#?
1 Answer
Dec 28, 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 equation in standard form "y=ax^2+bx+c#
#"then the x-coordinate of the vertex is"#
#x_(color(red)"vertex")=-b/(2a)#
#y=-3x^2-x+9" is in standard form"#
#"with "a=-3,b=-1,c=9#
#rArrx_(color(red)"vertex")=-(-1)/(-6)=-1/6#
#"substitute this value into the equation for y"#
#y_(color(red)"vertex")=-3(-1/6)^2+1/6+9=109/12#
#rArr(h,k)=(-1/6,109/12)" and "a=-3#
#rArry=-3(x+1/6)^2+109/12larrcolor(red)"in vertex form"#
