1. \( y=x^{2}+6 x+9 \)

Did you know that the quadratic equation \( y = x^2 + 6x + 9 \) can be rewritten in a much simpler form? It can be factored as \( y = (x + 3)^2 \), which means this equation represents a perfect square! This tells us that the graph of the function is a parabola that opens upwards and has its vertex at the point (-3, 0). In real-world applications, quadratic equations like this one can model various scenarios, from physics to finance. For instance, when determining the maximum area of a rectangular garden with fixed fencing, the dimensions can often be expressed using quadratic equations. Understanding where your parabola intersects the x-axis can give you critical insights into these kinds of problems!