Come up with your own twice-differentiable function and draw its graph without a calculator by analyzing its properties. These properties must be included in your presentation: zeros, symmetry, and first- and second-order derivatives, local and global extreme values, the concavity test, concave up, and concave down. Then, graph your function using your graphing calculator to verify your work. Images of both the hand-drawn graph and the graph on a calculator. Be sure to use precise mathematical language throughout the activity.