Section 1-1

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