Question

Question #7dfbc

Answer 1

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

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

Explanation:

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`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`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`