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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.

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2 Answers 2

up vote 2 down vote accepted

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 $x = -2$

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Thanks, this forum is a great learning source. –  Rakisbro Oct 23 '12 at 5:25

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

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

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