12/11/2013 BW 12/11 BW 12/11 BW 12/11 BW 12/11. 5 th Period: Enter silently as ALWAYS

Transcription

1 Wednesday, 12/11 and Thursday, 12/12 You Need: Fancy calculators YES CLICKERS! Normal math stuff (yes TB, just in case) BW 12/11 5 th Period: Enter silently as ALWAYS On your desk to be checked during BW: Assignment #69 --Pg. 253 #8-26 (25-32 was division. I will check those tomorrow) BW 12/11 BW 12/11 BW 12/11 Finish 1

2 Chapter 4 Test on Tuesday! Review Strategies for solving Quadratics today Questions on any homework assignment for the past few days? 4.9 Quadratic Inequalities tomorrow Test Review over the weekend and on Monday Number pairs of the form + and are complex conjugates. The product of complex conjugates is a real number! 5.) Find each quotient: Example: (4 1) = ) Find each quotient: # Complex Numbers part 2 LG: I will be able to solve quadratic equations and find all solutions real or imaginary. 2

3 Proceed as usual. If the discriminant is negative, simplify using! 2 +32= =0 No bterm! Move constants to the right! 2 +32=0 2 = 32 No bterm! Move constants to the right! 2 isn t a perfect square, so divide both sides by =0 2 = 32 = 16 No bterm! Move constants to the right! 2 isn t a perfect square, so divide both sides by =0 2 = 32 = 16 = 16 Take the square root of both sides and solve for x. 3

4 2 +32= =0 2 = 32 2 = 32 = 16 =± 16 Take the square root of both sides and solve for x. = 16 =± 16 Take the square root of both sides and solve for x. =± 16 =± 16 =±4 =2 = 3 =5 = ± 4 2 =2 = 3 =5 =2 = 3 =5 = ( 3)± ( 3) (4 2 5) 2 2 = ( 3)± ( 3) (4 2 5) 2 2 ± = 4

5 =2 = 3 =5 =2 = 3 =5 3± 9 40 = 4 ± = ± = ± = =2 = 3 =5 What does it mean to solve a quadratic equation? ± = = = ± = OR = ± We are finding out what x is equal to at a certain point! = = What are all the methods we ve learned for solving Quadratic Equations? 5

6 1: Solve by factoring Don t copy yet! We will go through each one and you can copy then! 2: Solve by factoring using a perfect square trinomial and taking the square root of both sides. 3: Solve by taking the square root of both sides if there is no bterm. 1: Solve by factoring Pros: Fast and easy (you all did awesome on the factoring quiz!) Cons: Only works with nice, pretty, factorable equations. +6+8=0 Copy 3 = : Solve by completing the square. 5: Solve by using the Quadratic Formula. 6: Solve by using the Zeros function on the calculator. 2: Solve by factoring using perfect square trinomials. Pros: Fast and easy Cons: Only works with perfect square trinomials. +6+9=1 3: Solve by taking the square root of both sides if there is no bterm. Pros: Super Fast and Super easy Cons: Only works when there is no bterm. 6 = =0 4: Solve by completing the square. Pros: You can ALWAYS complete the square! EVEN with imaginary solutions. Cons: There are a lot of steps. +2+3=0 5: Solve by using the Quadratic Formula. Pros: You can ALWAYS use it! EVEN with imaginary solutions. Cons: You have to hum an annoying song to remember it. And watch your negatives! +2+3=0 6

7 6: Solve by using the Zeros function on the calculator. Pros: Involves the least amount of brain power. Cons: Be careful! If your calculator gives you an answer of and you put that on your answer sheet I would mark it wrong. The correct answer is. Your calculator will turn it in to a decimal and viciously chop it off, even when inappropriate. +2+3=0 On the test I will say write your answer in simplest radical form or as a fraction as a hint that you can t use the calculator for that problem. Or I ll put it on the blue calculator portion. Standardized tests will do the same OR it will be multiple choice. How do we decide when to use each strategy? How do we decide when to use each strategy? I ve already tested you on factoring and later in the year you will be forced to use completing the square again. In other words, it doesn t matter to me which one you use. 3: Solve by taking the square root of both sides if there is no bterm. If there is no bterm, this method is the fastest. Step 1 of picking a strategy) Check for a bterm. On the next slides I will give you some ideas for decision making. 1: Solve by factoring 2: Solve by factoring using a perfect square trinomial and taking the square root of both sides. Possible step 1.5) If you are good at factoring, then after you see that there IS a bterm you can check an equation to see if it is factorable. Is it a perfect square trinomial? If not, set one side equal to zero and check to see what factors of acadd to get b. 3: Solve by taking the square root of both sides if there is no bterm. If there is no bterm, this method is the fastest. Check for a bterm. Completing the Square and the Quadratic Formula work for EVERY SINGLE PROBLEM. Even when the solutions are nonreal. I recommend picking one of these two methods to be your favorite if there is a bterm. Step 2) If there IS a bterm, then Complete the Square or use the Quadratic Formula. 7

8 Quadratic worksheet Pg. 253#39-44,56,67,71 8