Finding the symmetry axis of $f(x) = 2x^2 + 8x + 5$

Question

before I ask for anything I must admit I'm working hard to understand this beautiful subject. Thanks in advance. $$ f(x)= 2(x)^2+8x+5 $$ Acoording to the graph of this function, there is a x-axis symmetry. The problem is I can not prove it algebraically. Thanks again.

Answer 1

Do this $$f(x) = 2(x^2 + 4x) + 5 = 2(x^2 + 4x + 4) + 5 - 8 = 2(x + 2)^2 - 3.$$ Note that $f$ is insensitive to the sign of $x + 2$ so $f$ is symmetric about the line $x = -2$

Answer 2

$$f(x)=2\left(x^2+4x+\frac{5}{2}\right)=2((x+2)^2\pm...)$$

So it is symmetric on $x=-2$ which is parallel to $y$-axis.