My question is... When you say that we need to memorize the above outline of the model, are you talking about model part C(Validate and use the model)? or model part A(Obtain and represent Date), B (Obtain a Model), & C(Validate and use the model)?
This is the outline you are expected to memorize, and which will be used throughout the course.
Summary of Modeling Process, Version 3
A. Obtain and Represent Data
A1. Orient
A2. Observe
A3. Organize Data
A4. Graph
B. Obtain a Model
B1. Postulate
B2. Select Representative Points
B3. Obtain an equation for each selected point
B4. Solve the system of equations
B5. Substitute parameters
C. Validate and Use the Model
C1. Graph the model
C2. Quantify the comparison
C3. Pose and answer questions
C4. Do the science: relate the mathematics to the real world.
To Be Memorized
The above outline of the model is to be memorized. At any time during the course, on any test or quiz, you might be asked to write down this model and illustrate the meaning of one or more of the steps.
This outline will be more or less followed throughout the course.
What is the vertex exactly and how exactly do we find it?
We will see more about this in the last of the worksheets in Wednesday's handout, the Assignment 3 worksheet "Properties of Quadratic Functions".
A brief answer is:
y = a t^2 + b t + c is the equation of a parabola. The graph of this equation has the shape of a parabola (a parabola is a curve with the property that every point of the curve lies at the same distance from its focus and directrix, but the details of that definition and how it is related to the equation given here is a second-semester topic).
The parabola is symmetric about a vertical line. The point where the parabola intersects this vertical line is called the vertex. It is either the high or the low point of the parabola, depending on whether the parabola opens upward or downward.
The axis of symmetry is the line t = - b / ( 2 a), where a and b are the coefficients of t^2 and t.
You can find the y coordinate of the vertex by substituting this t value into the equation of the parabola.