Question

What is the vertex form of `y= 4x^2+2x+12`?

Answer 1

`y=4(x+1/4)^2+47/4`

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

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

`rArry=4(x^2+1/2x+3)`

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

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

`rArry=4(x+1/4)^2+4(-1/16+3)`

`rArry=4(x+1/4)^2+47/4larrcolor(red)"in vertex form"`