Respuesta :
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 )
= 2(x^2 + 4x) + 8
= 2 [ (x + 2)^2 - 4) + 8
axis of symmetry is x = -2 ( because of the (x + 2)^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 :
[tex]f(x)=2x^2+8x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
for a function g(x) with the form [tex]g(x)=a(x-h)^2+k,[/tex] the axis of symmetry is given by the following equation :
[tex]x-h=0~~~~\Rightarrow x=h.[/tex]
Now, from equation (i), we have
[tex]f(x)=2x^2+8x+8\\\\\Rightarrow f(x)=2(x^2+4x+4)\\\\\Rightarrow f(x)=2(x+2)^2+0.[/tex]
Therefore, the required axis of symmetry is given by
[tex]x+2=0\\\\\Rightarrow x=-2.[/tex]
Thus, the axis of symmetry for the function f(x) is x = -2.
