Question

identify and estimate the x- and y-values of the extrema. round to the nearest tenth if necessary.
relative maximum at (□, □)
minimum at (□, -4) and (2, □)

Explanation:

Step1: Analyze the relative maximum

The graph is symmetric about the y - axis. The relative maximum is at the peak of the graph on the y - axis. So the x - coordinate of the relative maximum is 0. By looking at the graph, the y - coordinate of the relative maximum (the height of the peak) can be estimated. From the grid, if we assume the grid lines are spaced such that the peak is at (0, 4) (since the minima are at y=-4 and the graph is symmetric).

Step2: Analyze the minima

The graph has two minima, symmetric about the y - axis. One of the minima is given as (2, - 4) (from the problem statement: Minimum at ( , - 4) and (2, )). Due to symmetry about the y - axis, the x - coordinate of the other minimum should be - 2 (because if (2, - 4) is a minimum, the point symmetric to it about the y - axis is (- 2, - 4)). And the y - coordinate of the minimum at (2, - 4) is - 4, so the second blank for the minimum at (2, ) is - 4.

Answer:

Relative maximum at \((0, 4)\)
Minimum at \((-2, - 4)\) and \((2, - 4)\)