Question

Which of the following reveals the minimum value for the equation 2x2 − 4x − 2 = 0?

2(x − 1)2 = 4
2(x − 1)2 = −4
2(x − 2)2 = 4
2(x − 2)2 = −4

Answer 1

2(x - 1)2 =4

Explanation:

Got a 100%

Good luck :)

Answer 2

`2(x-1)^(2)=4`

Explanation:

we have

`2x^(2) -4x-2=0`

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

Group terms that contain the same variable and move the constant to the other side

`2x^(2) -4x=2`

Factor the leading coefficient

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

`2(x^(2) -2x+1)=2+2`

`2(x^(2) -2x+1)=4`

Rewrite as perfect squares

`2(x-1)^(2)=4` -----> this is the answer

The vertex is the point (1,-4)