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12.3 Directed Graphs

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A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency matrix. If the nodes are connected, you place a 1 in the matrix. Ex: TO: n 1 n 2 n 3 n 4 FROM: A finite graph may need to include info about direction. We get a directed graph. *Flights work this way. n1n1 n2n2 n3n3 n4n4 From Long Beach to Orlando on Jet Blue

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Ex 1) Create the adjacency matrix. Chicago New York St. Louis TO: C N S FROM: What options do you have if you are making 2 flights? You would have the same matrix, but there would be two of them.

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2 nd x –1 is MATRIX EDIT choose 1: [A] enter dimensions 3 × 3 Now enter each element. When done, go 2 nd MODE to QUIT Calculate [A] 2 MATRIX NAMES 1: [A] matches! If we continued this, it would be a lot of multiplying. We can use our graphing calculators to speed things up!

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Ex 2) Suppose the nodes in the diagram represent people and the directed edges mean the first person knows the second person’s phone number. a) Interpret the diagram in a matrix. Al Betty Fred Charles David Ellen 2 nd person: A B C D E F 1 st person:

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Ex 2) cont… b)In how many ways can a message get from Betty to Ellen in 3 or fewer calls? (*Use your calculator!) A B C D E F No ways 2 ways 1 way so 3 different ways

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Ex 2) cont… c) Is it possible to get a message from Fred to Charles? If yes, what is the minimum number of calls? A B C D E F 1 call No way 2 calls 1 way Yes, 2 calls minimum

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Homework #1203 Pg 616 #1–5, 7, 9, 11, 15, 17–20, 22–32

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2.5 Graphing Quadratic Functions. There are two main methods for graphing a quadratic I. From Standard Form f (x) = ax 2 + bx + c Axis of Symmetry: Vertex:

2.5 Graphing Quadratic Functions. There are two main methods for graphing a quadratic I. From Standard Form f (x) = ax 2 + bx + c Axis of Symmetry: Vertex:

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