1. Do Now: Graph and state the type of graph and the domain and range if it is a function. Introduction to Analytic Geometry

2. Parabola Vertex: (0,0) Domain: (- ∞, ∞ ) Range: [0, ∞) Horizontal Parabola Vertex: (4,0) Not a function

3. Piecewise Domain: (- ∞, ∞ ) Range: (- ∞, -2], [1, ∞)

4. What is analytic geometry? AnalysisGeometry “ the study of figures in a space of a given number of dimensions and of a given type” (http://mathworld.wolfram.com)http://mathworld.wolfram.com Shapes Measures Congruence Proofs Mostly plane geometry Hyperbolic/spherical/projec tive “Analysis is the systematic study of real and complex- valued continuous functions.” (http://mathworld.wolfram.com)http://mathworld.wolfram.com Graphs Domain/Range Important Points Points of intersection (solutions to systems)

5. “The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry is also called coordinate geometry” (http://mathworld.wolfram.com)http://mathworld.wolfram.com

6. What should I already know how to do? Algebra manipulation of expressions: complete the square, factor, square binomials, expand powers of binomials Graph many function types: lines, conic sections, absolute values, exponential functions, logarithms, trigonometric functions Solve systems: elimination, substitution, matrices with row reduction

7. Algebra Complete the square. Square binomials Factor Expand binomials x 2 -2x +92x 2 -10x +5 (2x-4) 2 3x 2 -21x+36 (x+3) 4 =(x-1) 2 +8= 2(x-2.5) 2 -7.5 =4x 2 -16x+16 = 3(x 2 -7x+12) = 3(x-4)(x-3) = (1)x 4 +(4)3x 3 +(6)9x 2 +(4)27x+(1)81 =x 4 +12x 3 +54x 2 +108x+81 Pascal’s Triangle 1 1 2 1 1 3 3 1 1 4 6 4 1 (a+b) 2 = a 2 +2ab+b 2

8. Graphing Parent Functions

9. Exponential and Logarithmic Functions

10. Rational Functions

11. Trig functions

12. Conic Sections: Parabolas and Circles

13. Conic Sections: Ellipses and Hyperbolas

14. Solve Systems EliminationSubstitution Solution: (2, 0) (the point of intersection of the lines) Solution: (4, 13)

15. Solve systems Matrices Coefficient Matrix x = 3 x+y=2 x+2y+3z = 9 x = 3 y= -1 z=3

16. How can I do my best? Take notes Read the textbook Do the homework Keep a single sheet somewhere in your notes to write the formulas as you learn them.