Graph and compare the shapes and key features of the functions f(x)=(x+2)^2 and g(x)=2x+4 . In 3–5 sentences, explain how the two functions are similar and how they are different. Like a 9th grader.

Answer 1

The function \( f(x) = (x + 2)^2 \) is a quadratic function, which means its graph is a parabola that opens upwards. It has its vertex at the point (-2, 0) and is symmetric around the vertical line \( x = -2 \). On the other hand, the function \( g(x) = 2x + 4 \) is a linear function, represented by a straight line with a slope of 2, crossing the y-axis at (0, 4).

Both functions are similar in that they are expressions of \( x \), but they differ in their shapes: one is curved (the parabola), while the other is straight (the line). Additionally, \( f(x) \) has a minimum point at its vertex, whereas \( g(x) \) continues indefinitely in both directions without any turning points.