Question

What is the the vertex of `y = -12x^2+6x-18`?

Answer 1

`"vertex "=(1/4,-69/4)`

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"`

`"to express "y=-12x^2+6x-18" in this form"`

`"we can use the method of "color(blue)"completing the square"`

`• " ensure the coefficient of "x^2" term is 1"`

`• " add/subtract "(1/2"coefficient of x-term")^2`

`rArry=-12x^2+6x-18`

`color(white)(rArry)=-12(x^2-1/2x+3/2)`

`color(white)(rArry)=-12(x^2+2(-1/4)xcolor(red)(+1/16)color(red)(-1/16)+3/2)`

`color(white)(rArry)=-12(x-1/4)^2-69/4larr" in vertex form"`

`"with " h=1/4" and "k=-69/4`

`rArrcolor(magenta)"vertex "=(1/4,-69/4)`