1. Section 1-1 Models and Solving Equations

2. Section 6-1 Topics numerical models algebraic models graphical models solving factored equations fundamental connection grapher failure and hidden behavior

3. Numerical Models data is analyzed to gain insights into phenomena data is often in the form of a table or list sometimes the trends are easy to see but in some cases a more sophisticated tool is needed to do the analysis (computer spreadsheet)

4. Algebraic Models formulas and equations are created from numbers to make further predictions for unknown values some of the formulas we will use are ones we learned from other math courses or science courses (d = rt, A = lw, F = ma)

5. Graphical Models a visible representation of a numerical or algebraic model examples of graphical models: scatter plots, function graphing, charts, etc.

6. Solving Factored Equations zero-product property: if ab = 0, then a = 0 or b = 0. to solve an equation, move everything to one side so the other side equals 0, factor the polynomial, then set each factor equal to 0 and solve it if the poly will not factor then other methods are needed (quad. formula, graphing, etc.)

7. Fundamental Connection If a is a real number that solves the equation f (x) = 0, then these statements are equivalent a is a root (or solution) of the equation f(x) = 0 a is a zero of y = f (x) a is an x-intercept of the graph of y = f (x) (x – a) is a factor of f (x)

8. Grapher Failure and Hidden Behavior sometimes the graphing calculator will have problems correctly showing the graph you want to see for a function maybe the window is too large or too small the grapher has trouble with functions with a vertical asymptote maybe there are “hidden” zeros for a graph