To find the vertex of the graph and determine whether or not it is a maximum or minimun, we proceed as follows:
Step 1: Identify the x and y coordinates at the turning point of the graph, that is, at the the point where the graph changes direction from upwards to downwards OR downwards to upwards, as the case may be.
From the graph given, we see that the graph changes direction from downwards to upwards at the point where x = 0 AND y = -1
Therefore, the vertex of the graph is at the point where x = 0, and y = -1 OR the coordinate (0, -1 )
Step 2: Identify the nature of the trend of the graph at the vertex, that is, as it passes through the turning point.
Now, if the graph goes from a downward trend to an upward trend as it passes the turning point, then the vertex point is a MINIMUM
However, if the graph goes from an upward trend to an downward trend as it passes the turning point, then the vertex point is a MAXIMUM
Therefore, from the above explanation, the graph in question has only a MINIMUM, because the graph goes from a downward trend to an upward trend as it passes the turning point at the vertex