Question

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

Answer 1

Answer:

$2(x-1)^{2}=4$

Step-by-step explanation:

The options of the question are

2(x − 1)2 = 4

2(x − 1)2 = −4

2(x − 2)2 = 4

2(x − 2)2 = −4

we have

$2x^{2} -4x-2=0$

This is a vertical parabola open upward

The vertex represent the minimum value

The quadratic equation in vertex form is

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

so

Convert the quadratic equation in vertex form

Factor 2 leading coefficient

$2(x^{2} -2x)-2=0$

Complete the squares

$2(x^{2} -2x+1)-2-2=0$

$2(x^{2} -2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

The vertex is the point (1,-4)

Move the constant to the right side

$2(x-1)^{2}=4$