pencil, highlighter, GP notebook, calculator, textbook U10D1 Have Out: Bellwork: Use the Rational Root Theorem to find all zeros of by listing all the possible rational zeros. Sketch a graph of y = P(x). total:

Possible rational zeros q Possible rational zeros factors of 9 ±1, ±3, ±9, factors of 2 ±1, ±2 +1 +1 1 Start with x = ____ 2 5 –7 –9 9 +1 +2 +7 +0 –9 +1 1 2 7 –9  +1

Possible rational zeros q p Possible rational zeros factors of 9 ±1, ±3, ±9, factors of 2 ±1, ±2 –3 Start with x = ____ -6 1 2 7 –9 +1 –2 3 +1 –6 –3 +9 x – 1 –3 2 1 –3  +1 2x 2x2 –2x + 3 + 3x –3 +1

zeros: x = ______________ +1 set = 0 y +1 ZPP x – 1 = 0 x + 3 = 0 2x + 3 = 0 x = 1 x = –3 (0, 9) –3, 1, 1 zeros: x = ______________ +3 x (–3, 0) (1, 0) +1 labeled x–intercepts +1 labeled y–intercepts total: +1 end behavior +1 bounce

You are going to like this chapter... because… We are going to play games! Let’s start with a game of… ROCK PAPER SCISSORS Rochambeaux – “_______ _______ ___________”

Let's play!!! ROCK PAPER SCISSORS Rochambeaux – “_______ _______ ___________” Part 1: Two Players You and your table partner are going to pair up to play Rochambeaux. Decide between your partner and you who will be Player A or Player B. Fill in your names on the worksheet. Directions: You will play 18 rounds of Rochambeaux. The twist is that Player A wins if both players match, while player B wins if they do not match. Record who wins, A or B, on your worksheet. Also record the number of times A wins and the number B wins below your data. Let's play!!!

What you are observations? Player B won the most. There were more mis–matches than matches. What happened? These are called _________ Probabilities because they are what was experienced. Empirical On the other hand… Theoretical expect ___________ Probabilities – what we _________ to happen.

AREA MODEL An area model shows all the __________ possibilities in an organized form. theoretical Label the sides of the model using the symbols: R = rock P = paper S = scissor PLAYER A 9 # of possible outcomes: ___ R P S 3 # of matches (A wins): ___ R RR RP RS # of no matches (B wins): ___ 6 PLAYER B P RP PP PS S RS PS SS Recall the formula for probabilities: # of outcomes in the event P (_____) = ________________________ event total # of possible outcomes P (A wins) = ___ P (B wins) = ___

P (A wins) = ___ P (B wins) = ___ _________ ______ - the amount we would ________ to win or lose on ________ if we played the game ______ times. Expected value expect average many Based on the __________ probabilities, for 18 trials, the _________ ______ for: theoretical expected value # A wins = 18 = 6 # B wins = 18 = 12

TREE DIAGRAM - used to determine the probability of ________ outcomes from all the ________ outcomes. individual possible PLAYER A  R P S PLAYER B  R P S R P S R P S A B B B A B B B A There are __ pathways to the end, so there are __ outcomes. 9 9 Write “A” at the end of each path where A wins. Put “B” at the end of each path where B wins. likely Since all paths (for this scenario) are equally ______, then P (A wins) = ___ P (B wins) = ___

Part 1: Three Players This time, get in teams of 3 persons. Decide in your group who will be Player A, B or C. Fill in your names on the worksheet. Directions: You will play 27 rounds of Rochambeaux. Here’s the twist: Player A wins if _____ match, player B wins if _______ match, and player C wins if ______ match. Record who wins, A, B or C, on your worksheet. all 3 2 of 3 none empirical Based on these 27 trials, the _________ probabilities are: P (A wins) = ___ P (B wins) = ___ P (C wins) = ___ 27 27 27 Fill in the information above that your group EXPERIENCED.

What you are observations? Player B won the most. There were more 2 of 3 matches than either all matches or no matches. So, you just recorded the empirical probabilities, that is, what you experienced. Theoretically, what would the probabilities have been?

(There are many more branches!!!!) On a separate sheet of paper, make a tree diagram or an organized list to find the __________ probabilities for each player winning. theoretical Player A  Player B  Fill in all the branches and details similar to the one we made earlier. (There are many more branches!!!!) Player C  P(all matches) = P(2 of 3 matches) = P(no matches) =

Player A R P S Player B R P S R P S R P S R P S R P S R P S R P S R P Player C P(all matches) = P(2 of 3 matches) = P(no matches) =

Finish the tree diagram, then work on PM 4 – 8, 10

Do not move until everyone’s name is called. It’s time to Change Seats! Do not move until everyone’s name is called.