Question

What is the minimum value of the function

Answer 1

`x^(2) - 6 + 7 = 0`
a = 1; b = - 6, c = 7
Δ = b² - 4.a.c
Δ = (-6)² - 4.1.7
Δ = 36 - 28
Δ = 8

Calculate the minimum value:


`Y_(v) = (-\Delta)/(4a)`


`Y_(v) = (-8)/(4*1)`

`Y_(v) = (-8)/(4)`

`\boxed{Y_(v) = -2}`

Answer:

`\boxed{\textcircled{ A } = -2}`

Follow the attachment (graphic):

Answer 2

`x^2-6x+7=x^2-6x+9-2=(x-3)^2-2`

is a parabola with its vertex at
`(3,-2)`, which means the minimum value is
`-2`.