Question

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

Answer 1

`y=-3(x+1/6)^2+109/12`

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"`