What is the vertex form of y=-3x^2-x+9y=−3x2−x+9?

1 Answer
Jim G.
Dec 28, 2017

y=-3(x+1/6)^2+109/12y=−3(x+16)2+10912

Explanation:

"the equation of a parabola in "color(blue)"vertex form"the equation of a parabola in 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"

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