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

1 Answer
Jun 7, 2018

Answer:

#(-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]}