Question

How do you find the range of `f(x)= -6(x+4)^2-12`?

Answer 1

`(-oo,-12]`

Explanation:

`"we require to find the vertex and if max/min"`

`"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+b)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`y=-6(x+4)^2-12" is in vertex form"`

`"with vertex "=(-4,-12)`

`"to determine if vertex is max/min"`

`• " if "a>0" then minimum "uuu`

`• " if "a<0" then maximum "nnn`

`"here "a=-6" hence maximum at "(-4,-12)`

`"range is "(-oo,-12]`
graph{-6(x+4)^2-12 [-40, 40, -20, 20]}