Answer: see below
Explanation:
To complete the table, we need to evaluate the function f(u) = u² + 2u + 3 for the given values of u.
f(u) U
-20 (-20)² + 2(-20) + 3 = 403
-10 (-10)² + 2(-10) + 3 = 117
0 0² + 2(0) + 3 = 3
10 10² + 2(10) + 3 = 123
The table can be filled as follows:
f(u) U
403 -20
117 -10
3 0
123 10
The function f(u) = u² + 2u + 3 is a quadratic function, which has a parabolic shape. The coefficient of u² is positive, which means the parabola opens upward. The vertex of the parabola is at the point (-1, 2), which is the minimum point of the function.
As u increases or decreases from 0, the function increases. This is reflected in the table, where we see that the values of f(u) increase as u moves away from 0.
The table gives us a set of ordered pairs that represent the function f(u) for the given values of u. These ordered pairs can be plotted on a coordinate plane to draw the graph of the function.