1. **State the problem:** Simplify or analyze the quadratic expression $x^2 - 4x + 8$. 2. **Recall the quadratic form:** A quadratic expression is generally written as $ax^2 + bx + c$. 3. **Identify coefficients:** Here, $a=1$, $b=-4$, and $c=8$. 4. **Find the vertex form:** Use the formula for the vertex $x$-coordinate: $x = -\frac{b}{2a}$. 5. Calculate $x$-coordinate of vertex: $$x = -\frac{-4}{2 \times 1} = \frac{4}{2} = 2$$ 6. Find the $y$-coordinate by substituting $x=2$ into the expression: $$y = (2)^2 - 4(2) + 8 = 4 - 8 + 8 = 4$$ 7. **Vertex form:** The vertex is at $(2,4)$, so the expression can be rewritten as: $$x^2 - 4x + 8 = (x - 2)^2 + 4$$ 8. **Interpretation:** This shows the parabola opens upwards with vertex at $(2,4)$ and minimum value 4. **Final answer:** The expression in vertex form is $$ (x - 2)^2 + 4 $$.