Question

Complete the square to determine the minimum or maximum value of the function defined by the expression.

x2 − 12x − 2

A) maximum value at 38 B) minimum value at 38 C) maximum value at −38 D) minimum value at −38

Answer 1

Option D. minimum value at −38

Explanation:

we have

`x^(2)-12x-2`

Let

`y=x^(2)-12x-2`

Complete the square

`y+2=x^(2)-12x`

`y+2+36=(x^(2)-12x+36)`

`y+38=(x^(2)-12x+36)`

`y+38=(x-6)^(2)`

`y=(x-6)^(2)-38` ------> equation of a vertical parabola in vertex form

The vertex is the point
`(6,-38)`

The parabola open upward-----> the vertex is a minimum

therefore

minimum value at −38