1) \( x^{2}+4 x+4= \)

This expression is a perfect square trinomial! It can be factored elegantly as \( (x + 2)^2 \). This means that instead of dealing with the quadratic in standard form, you can quickly understand its behavior as a square. When graphed, it represents a parabola that opens upwards and has its vertex at the point (-2, 0). For real-world application, quadratics like this pop up in various fields, including engineering when dealing with projectile motion, and in finance for profit maximization problems. Understanding how to manipulate them can help predict outcomes and make informed decisions in real-life scenarios, like determining the maximum height of a product’s launch!