How do you find the axis of symmetry, and the maximum or minimum value of the function #y = -x^2 - 3x -5#?

1 Answer
Oct 24, 2017

Axis of symmetry is # x =-1.5 #, maximum value is #-2.75#
and minimum value extends to #-oo#.

Explanation:

#y= -x^2-3x-5 or y= -(x^2+3x) -5 # or

#y=-(x^2+3x+1.5^2)+2.25 -5 # or

#y=-(x^2+1.5)^2-2.75 # . This is vertex form of

equation #y=a(x-h)^2+k ; a=-1 ,h=-1.5 ,k=-2.75 #

Therefore vetex is at #(h,k) or (-1.5, -2.75)#

Axis of symmetry is #x= h or x =-1.5 ; a# is negative,

so parabola opens downward. Therefore vertex is the

maximum point #(-1.5, -2.75) :.# Maximum value is #-2.75#

and minimum value extends to #-oo#.

graph{-x^2-3x-5 [-20, 20, -10, 10]} [Ans]