The function \( f(x) = (x+2)^2 \) is a quadratic function, which results in a parabolic shape that opens upwards. Its vertex is at the point (-2, 0), indicating the lowest point on the graph. In contrast, the function \( g(x) = 2x + 4 \) is a linear function, represented by a straight line with a slope of 2 and a y-intercept at (0, 4).
The key similarities between the two functions include that they both represent polynomial functions and are continuous over all real numbers. However, they differ significantly in shape: \( f(x) \) has a curved parabolic form, while \( g(x) \) is a straight line. Additionally, the quadratic function can have a vertex and exhibits a minimum point, while the linear function does not have any extremum points and continues infinitely in both directions.
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