Question

How do you find the vertex of `y= x^2 - 6x + 14`?

Answer 1

Vertex`" "->(x,y) ->(3.5)`

Explanation:

The question does not define the method to be used so you have freedom of choice.

Let me show you a 'sort of' cheat method. Actually it forms part completing the square but does not take to the end of the process.

Consider standard form`" " y=ax^2+bx+c`

Write this as:`" "y=a(x^2+b/ax)+c`

Then you have `x-("vertex")=(-1/2)xxb/a`

For this question:
`a=1`
`b/a =(-6)/1 =-6`

`=>" "color(blue)(x_("vertex")=(-1/2)xx(-6) = +3)`

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By substitution

`color(brown)(y=x^2-6x+14 color(blue)(->y_("vertex")=(3)^2-6(3)+14))`

`color(blue)(y_("vertex")=9-18+14=5)`

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