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.