1. The term "concave up" describes the shape of a graph of a function. 2. A graph is concave up if the curve bends upward like a U shape. 3. Mathematically, this means the second derivative of the function, denoted as $$f''(x)$$, is positive: $$f''(x) > 0$$ for all x in the interval. 4. This positive second derivative indicates that the slope of the tangent line is increasing as x increases. 5. Graphically, if you draw a line segment between any two points on the graph, the graph lies below that line segment when concave up. 6. This shape suggests the function is accelerating upwards, like a bowl holding water.