standard_description: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)
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