Question

What is the axis of symmetry for f(x)=2x2+8x+8

Answer 1

2x^2 + 8x + 8
= 2(x^2 + 4x) + 8
= 2 [ (x + 2)^2 - 4) + 8

axis of symmetry is x = -2 ( because of the (x + 2)^2 )

Answer 2

Answer: The axis of symmetry for the function f(x) is x = -2.

Step-by-step explanation: We are given to find the axis of symmetry for the following function :

`f(x)=2x^2+8x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

for a function g(x) with the form
`g(x)=a(x-h)^2+k,` the axis of symmetry is given by the following equation :

`x-h=0~~~~\Rightarrow x=h.`

Now, from equation (i), we have

`f(x)=2x^2+8x+8\\\\\Rightarrow f(x)=2(x^2+4x+4)\\\\\Rightarrow f(x)=2(x+2)^2+0.`

Therefore, the required axis of symmetry is given by

`x+2=0\\\\\Rightarrow x=-2.`

Thus, the axis of symmetry for the function f(x) is x = -2.