Question

Determine the axis of symmetry for the function f(x)= -2(x + 3)2 - 5.

Answer 1

Answer:-2.125

Explanation:

1. simplify the function

-2(x+3)2-5

(-2x-6)2-5

(-4x-12)-5

-4x-17

2. formula for axis of symmetry: -b/2a

a=-4 b=-17

-(-17)/2(-4)=17/-8=-2.125

Answer 2

The axis of symmetry for the function f(x) is x=-3.

Explanation:

The vertex form of a quadratic function is

`y=a(x-h)^2+k` .... (1)

Where, (h,k) is vertex and x=h is the axis of symmetry.

The given function is

`f(x)=-2(x+3)^2-5` .... (2)

From (1) and (2), we get

`a=-2,h=-3,k=-5`

The axis of symmetry is

`x=h`

Substitute h=-3 in the above equation.

`x=-3`

Therefore the axis of symmetry for the function f(x) is x=-3.