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.(4 points)
The function f(x)=(x+2)2 is a quadratic function that opens upwards and has a vertical shift of 2 units to the left. It has a vertex at the point (-2,0) and is symmetric about the vertical line x=-2. On the other hand, the function g(x)=2x+4 is a linear function with a positive slope of 2. It is a straight line that intersects the y-axis at (0,4).
Both functions have a similar shape to some extent, as they both increase as x increases. However, the quadratic function has a curved shape, while the linear function has a straight shape. Another key difference is that the quadratic function has a minimum point (vertex) at (-2,0), while the linear function does not have any minimum or maximum points. Additionally, the quadratic function is symmetric about the vertical line x= -2, whereas the linear function does not have any symmetry.