- Line of symmetry
- Coordinate graphs of quadratics relation
- Finding line of symmetry from data, from equation
- Secant lines and slopes
- Locatring the vertex. and slopes of secant lines.

- Functions rule relating variables
- function notation x -> f(x)

Tutorial on Functions (numerical & algebraic)

Tutorial on Functions (Visual/Graphical)

Static vs. Dynamic visualizations

Winplot: a tool for visualizing functions

**[Optional- Read:The parabola and squares.****Ratio of Length of verticals :: ratio of squares on horizontals]**

**Visualizing Algebra, Motion and Change****time vs. position****time vs velocity**

**[Optional- Read:Analytic geometry- Descartes and Fermat]**- Section 10.1 - Quiz

**Motion and distance traveled by a falling object****Visualize:**

**constant velocity connected to area of rectangle**

**constantly increasing velocity connected to area of a triangle.**

**Motion and position (cannon balls)****Visual connections:****Horizontal motion- constant velocity.****Vertical motion- constantly increasing velocity.****Combined- parabola!**

**Tangent line:**

**Visualize: Position and velocity.**

**Linear position, velocity is slope.****Quadratic position, velocity is slope of tangent.****Estimation of slope**

**From graphing****From slopes of Secant lines**

**Area of a region****Squares and Rectangles****Triangles****Circles (estimations and Archimedes)****Estimations for parabolic region.**- Section 10.2 - Quiz
**10.3, 10.4****Newton/Cauchy:****Newton: Tangent lines, velocity, and the "derivative."****Finding slope of tangent (newton/cauchy)****Finding "instantaneous velocity"****Abstraction of common numerical measurement procedure:**

**The derivative is a number which is**

**determined at "the limit" of numbers corresponding to slopes of secants lines with short bases (of length dx) and/or**

**average velocities with short time intervals (of duration dt).**