standard_description: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
problem_activity: Task
Let $P = (0,1)$ and $Q = (1,2)$ in the $(x,y)$ plane.
Show that there is a unique linear function described by the equation $y = mx + b$ whose graph contains $P$ and $Q$: find $m$ and $b$.
Show that there is a unique exponential function described by the equation $y = ab^x$ whose graph contains $P$ and $Q$: find $a$ and $b$.
Show that there is more than one quadratic function described by the equation $y = ax^2 + bx
+c$ whose graph contains $P$ and $Q$.


aligns: no