1. \( x^{2}+8 x+12 \)

To solve the quadratic equation \( x^{2}+8x+12 \), you can factor it. Look for two numbers that multiply to 12 and add to 8. Those numbers are 6 and 2, allowing us to rewrite the equation as \( (x+6)(x+2) = 0 \). Setting each factor to zero gives us the solutions: \( x = -6 \) and \( x = -2 \). If you're plotting this on a graph, the parabola opens upwards, and its vertex is the lowest point. It intersects the x-axis at the points we found, -6 and -2, while the vertex can be calculated using the formula \( -b/(2a) \), which yields \( -4 \) for x and substituting back gives the vertex's y-value.