Question

What is the vertex form of `y= - 3x^2 +7x - 15`?

Answer 1

`y=-3(x-7/6)^2-131/12`

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"`

`"to obtain this form use the method of "color(blue)"completing the square"`

`• " coefficient of "x^2" term must be 1"`

`rArry=-3(x^2-7/3x+5)`

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

`rArry=-3(x^2+2(-7/6)xcolor(red)(+49/36)color(red)(-49/36)+5)`

`color(white)(rArry)=-3(x-7/6)^2-3(-49/6+5)`

`color(white)(rArry)=-3(x-7/6)^2-131/12larrcolor(red)"in vertex form"`