Monday: Announcements • Unit 5 Retest: Deadline is Friday at 8:35am. • Must have test correction complete to retest and come to at least one tutorial session for help. • Dropping Lowest Grade (40% category)! • Final Exam Review will be graded and is the last grade for the 3rd 6 weeks • Answer key is posted on-line, but you MUST show work to get credit. • No Factoring Quiz this week due to Final Exams Algebra 2 Fall Semester Exam Review Test Format • Final Exam is all calculator • 34 Questions • All Multiple Choice Key Concepts on Test • • • • • Solving Equations and Inequalities Domain/Range/Functions Parent Function graphs Direct and Inverse Variation problems Transformations – Order of transformations – Graphing using transformations • Linear Regression (STAT) • Data Analysis (zoom 9) Key Concepts on Test • Quadratic Equations – – – – – – – Simplify positive and negative radicals Graphing (vertex point, AOS, solutions) Factoring Methods Square Roots Method Complete the Square Discriminant Quadratic Formula • Vertex Format/Complete the Square Key Concepts on Test • Writing Quadratic Equations – Vertex Point and another Point – Solutions and another Point – Quadratic Regression Calculator • Can be used to solve 60% of your test • Know the following: – – – – How to graph 2nd trace (vertex and zeros) Linear & quadratic regressions Plug in numbers (watch out for negatives) Testing Hints • • • • If you can graph it in the calculator, then do so Double graphing to compare Be careful of negatives when solving equations Questions with graphs! Look carefully at each graph so you select the one you really want • Plug in solutions to calculator to check In Class Review: Today • • • • • • • Equations and Inequalities Relations/Functions Domain/Range Variations Transformations Data Analysis/Regression Quadratic Word Problems 2( x 4) 4( x 6) 2x 8 4x 24 2x 4x 24 8 6x 16 16 8 x 6 3 BIG DIFFERENCE If you multiply or divide each side of an inequality by a negative number then the order of the inequality must be switched. EXAMPLE 4 Solve an inequality with a variable on both sides Solve 5x + 2 > 7x – 4. Then graph the solution. 5x + 2 > 7x – 4 – 2x + 2 > – 4 – 2x > – 6 x<3 Write original inequality. Subtract 7x from each side. Subtract 2 from each side. Divide each side by – 2 and reverse the inequality. ANSWER The solutions are all real numbers less than 3. The graph is shown below. Relations Ordered Pairs (2, 3) (-3, 1) (1, -2) Graphs Tables X 2 -3 1 Y 3 1 -2 X Mapping Y 2 3 -3 1 1 -2 Example : • Given the following ordered pairs, find the domain and range. Is it a function • {(4,5), (-2,3), (5,6)} • Domain is {-2, 4, 5} • Range is {3, 5, 6} • YES, no duplicated x-values 8 Domain 6 (, ) 4 Range 2 [2, ) -5 5 -2 Domain 6 4 (,3] Range [1, ) 2 -5 5 Domain (, ) Range [0, ) Direct Variation As one variable increases, the other must also increase ( up, up) OR As one variable decreases, the other variable must also decrease. (down, down) Direct Variation • Find y when x = 6, if y varies directly as x and y = 8 when x = 2. y1 y2 x1 x2 y1 8 6 2 2 y1 48 y1 24 Inverse Variation As one variable increases, the other decreases. (or vice versa) Inverse Variation Find x when y = 5, if y varies inversely as x and x = 6 when y = -18. x1 y1 x2 y2 x1 21.6 x1 5 6 18 5x1 108 y af ( x c) d Rx VS or VC Ry (+) Up (-) Down (+) Left (-) Right Example 1 f ( x) x 5 3 Right 5 , Up 3 Example 2 f ( x) x 2 1 Left 2 , Ry , Down 1 Example 3 f ( x) 2 | x 3 | 7 R 3 , VS 2, Rx , U 7 Domain (, ) Transformations Range L 2, VS 2 [0, ) Data Analysis Height (meters) 15 30 45 60 75 90 105 Distance Km 13.833 19.562 23.959 27.665 30.931 33.883 36.598 STAT Plotter “ON” Zoom 9 What Parent Function?? Weeks Experience 4 7 8 1 6 3 5 2 9 6 Speed (wpm) 33 45 49 20 40 30 38 22 52 44 42 y-axis 45 40 35 30 25 y 4.064 x 16.300 20 15 10 r .986 5 0 1 2 3 4 5 6 7 8 9 10 x-axis 7 Application Problems y .0035 x 2 x 5 2 • Need to change the viewing WINDOW • x-min, x-max • y-min, y-max Put in Calculator Window Max Height (Vertex Pt) 290.7 Max Distance (Zero) 573.9