Question

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

Answer 1

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]