Interpreting Nonlinear Graphs in Context

On the SAT, you'll see graphs of real-world situations and must interpret their features: | Graph feature | Mathematical meaning | Real-world meaning | |---|---|---| | Y-intercept | f(0) | Starting/initial value | | X-intercept(s) | f(x) = 0 | When the quantity is zero | | Vertex (max) | Highest y-value | Maximum height/profit/amount | | Vertex (min) | Lowest y-value | Minimum cost/distance/time…

The SAT often asks questions like: - "During what time interval was the height increasing?" → Where is the graph going up? - "What was the maximum revenue?" → What is the y-coordinate of the vertex? - "When did the ball hit the ground?" → Where does the graph cross the x-axis (after launch)? - "What does the y-intercept represent?" → What's the value at x = 0 (often time = 0)?

Example: A graph shows a ball's height h (feet) vs time t (seconds). The graph is a downward parabola with vertex at (2, 64) and x-intercepts at (0, 0) and (4, 0). Interpret these features.