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Answer 1 · 2016-08-11T12:56:47

$color(purple)("Bit of a cheat method")$

The axis of symmetry is $x=4 1/2$

Multiplying out the brackets we have:

$9x-x^2=14$

Presenting this in standard form gives:

$y=x^2-9x+14$

The next bit is part of the process of completing the square

$x_("vertex")=(-1/2)xx-9=+4 1/2$

So the axis of symmetry is $x=4 1/2$
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$color(red)("Deeper insight into the process:")$

Consider $y=ax^2+bx+c$

Write as: $=a(x^2+b/ax)+c$

$x_("vertex")=(-1/2)xxb/a$

In your case the value of a is +1 so

$color(brown)((-1/2)xxb/a)color(blue)(" "->" "(-1/2)xx(-9)/(+1) = + 4 1/2$