Question

How do you write this equation into the vertex form `f(x) = x^2+4x+6`?

Answer 1

`f(x)=(x+2)^2+2`

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 "color(blue)"complete the square"`

`f(x)=x^2+4x color(red)(+4)color(red)(-4)+6`

`color(white)(f(x))=(x+2)^2+2larrcolor(blue)"in vertex form"`