Question

How do you write the quadratic function `y=x^2+12x+6` in vertex form?

Answer 1

`y=(x+6)^2-30`

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 constant.

`"for a quadratic in standard form " ax^2+bx+c`

`x_(color(red)"vertex")=-b/(2a)`

`x^2+12x+6" is in this form"`

`"with " a=1,b=12,c=6`

`rArrx_(color(red)"vertex")=-12/2=-6`

`"substitute this value into the equation for y"`

`y_(color(red)"vertex")=(-6)^2+(12xx-6)+6=-30`

`rArrcolor(magenta)"vertex "=(-6,-30)`

`rArry=(x+6)^2-30larrcolor(red)" in vertex form"`