The expression $2x^2 - 8x + 4$ is a quadratic function. If you want to simplify or solve it, I can assist with various methods, such as factoring, completing the square, or using the quadratic formula. Let's break it down:

Simplifying the Expression:

The greatest common factor (GCF) of all the terms is 2. Let's factor that out first:

$2(x^2 - 4x + 2)$

Now, the expression is simplified, but it cannot be factored further using simple factorization.

Solving the Equation $2x^2 - 8x + 4 = 0$:

If you're looking to solve this quadratic equation, we can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the equation $2x^2 - 8x + 4 = 0$, the coefficients are:

• $a = 2$
• $b = -8$
• $c = 4$

Now, applying these values to the quadratic formula:

$x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(2)(4)}}{2(2)}$ $x = \frac{8 \pm \sqrt{64 - 32}}{4}$ $x = \frac{8 \pm \sqrt{32}}{4}$ $x = \frac{8 \pm 4\sqrt{2}}{4}$ $x = 2 \pm \sqrt{2}$

Thus, the two solutions are:

$x = 2 + \sqrt{2} \quad \text{or} \quad x = 2 - \sqrt{2}$

Would you like more details on any specific step or clarification?

Related Questions:

1. How do you complete the square for $2x^2 - 8x + 4$?
2. Can you graph the function $y = 2x^2 - 8x + 4$?
3. What are the applications of solving quadratic equations?
4. Can you explain how to approximate $\sqrt{2}$ for practical calculations?
5. What are the properties of the parabola represented by $y = 2x^2 - 8x + 4$?

Tip:

When solving quadratic equations, always check whether factoring is possible before applying the quadratic formula—it can save time!