Question

How do you find the vertex of `y= 3x^2 +12x-6`?

Answer 1

`"vertex "=(-2,-18)`

Explanation:

`"Given the quadratic in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c;a!=0`

`"then the x-coordinate of the vertex can be found using"`

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

`y=3x^2+12x-6" with "a=3,b=12,c=-6`

`rArrx_("vertex")=-12(6)=-2`

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

`y_("vertex")=3(-2)^2+12(-2)-6=-18`

`rArrcolor(magenta)"vertex "=(-2,-18)`