Question

A second degree polynomial function g is such that g(0)=g(6) and has a minimum of -2
Practice your variation table

Answer 1

To create a variation table for a second-degree polynomial function, we need to find the critical point(s) of the function, the intervals, and the sign of the function in each interval.

Given that g(0) = g(6) and g has a minimum of -2, we can deduce that the vertex of the parabola representing the function is located at (3, -2). This is because the midpoint between x = 0 and x = 6 is x = 3, and the function has a minimum at this value.

Now, let's create a variation table with intervals and the sign of the function in each interval:

Intervals | x < 3 | 3 < x < 6 |
------------------------|--------|------------|
Sign of g(x) | - | + |

In the interval x < 3, the sign is negative because the function is decreasing towards the left side of the vertex.

In the interval 3 < x < 6, the sign is positive because the function is increasing towards the right side of the vertex.

Note: Since the given polynomial function does not have an expression provided, we can only determine the sign of the function based on the given conditions.