standard_description: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Task
Consider three points in the plane, $P=(-4, 0), Q=(-1, 12)$ and $R=(4, 32)$.
Find the equation of the line through $P$ and $Q$.
Use your equation in (a) to show that $R$ is on the same line as $P$ and $Q$.
Show that $P, Q$ and $R$ are on the graph of the equation $y = x^3 + x^2 - 12 x$.
Is it possible for $P, Q$ and $R$ to all lie on a parabola of the form $y=ax^2+bx+c$?


aligns: no