Question

What is the vertex form of `y= 12x^2-14x-6`?

Answer 1

`y=12(x-7/12)^2-121/12`

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 constant.

`"Rearrange " y=12x^2-14x-6" into this form"`

`"Using the method of "color(blue)"completing the square"`

`y=12(x^2-7/6x-1/2)larr" coefficient of " x^2" is unity"`

`y=12[(x^2-7/6xcolor(red)(+49/144))color(red)(-49/144)-1/2]`

`color(white)(y)=12[(x-7/12)^2-121/144]`

`rArry=12(x-7/12)^2-121/12larrcolor(red)" in vertex form"`