9.1.1 What else can I solve?

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1 CCA Ch 9: Solving Quadratics and Inequalities Name Team # What else can I solve? Solving Quadratic Equations 9-1. USE THE ZERO PRODUCT PROPERTY TO SOLVE FOR X. a b c intercept(s): -intercept(s): -intercept(s): 9-2. a. Graph b. c. Check 9-1. b & c a. Work Space 9-3. a. Is Kira correct? Eplain how ou know: b. What did Kateln mean? Use our graphing calculator to estimate the solution(s):

2 c. SKIP d. Complete the square: Use Graphing Form to solve for : Graphing Form: Solution(s): How do our calculated solutions in part d compare to our estimates in part b? Eact Solutions = Approimate Solutions = e. Complete the square: Use Graphing Form to solve for : Graphing Form: Eact Solution(s): Approimate Decimal Forms: f. Check our answers b graphing in our graphing calculator.

3 9-4. Complete the square and solve. a. Complete the square: Use Graphing Form to solve for : Graphing Form: Eact Solution(s): Approimate Decimal Forms: b. Complete the square: Use Graphing Form to solve for : Graphing Form: Eact Solution(s): Approimate Decimal Forms: 9-5. Check our answers from 9-4 b using the graph and/or table in our graphing calculator.

4 9.1.2 What if it s not factorable? Introduction to the Quadratic Formula a b. m 2 12m 37 0 Graphing Form: Perfect Square Form: Number of Solutions: c. 4 p 2 36p 81 Graphing Form: Perfect Square Form: Number of Solutions: d. k 2 3k 9 0 Graphing Form: Perfect Square Form: Number of Solutions: Graphing Form: Perfect Square Form: Number of Solutions: a a = b = c = b. b b2 4ac 2a Eact (or Radical) Form: Approimate Decimal Form:

5 c. Verif our solutions b graphing and finding the zeros on our graphing calculator a. What are all the methods ou can use to solve quadratic equations? b. See the Math Notes bo on the net page in our book to see wh the Quadratic Formula works Use the Quadratic Formula Check with our graphing calculator. a a = b = c = b a = b = c = Eact Solution(s): Approimate Solution(s): Eact Solution(s): Approimate Solution(s):

6 c a = b = c = d a = b = c = Eact Solution(s): Approimate Solution(s): Eact Solution(s): Approimate Solution(s): Check our solutions for parts a, b, c & d b graphing and finding the zeros Learning Log Quadratic Formula Describe how to use the Quadratic Formula to someone who has never used it before. Be sure to include warnings on where possible mistakes could be made.

7 9.1.3 What if the equation is not in standard form? More Solving Quadratic Equations a. Solve b Factoring and using the ZPP: b. Solve using the Quadratic Formula: c. Did the solutions in parts a and b match? Wh does this make sense? Use the Quadratic Formula to solve a b

8 c d Check our solutions for parts a, b, c & d b graphing and finding the zeros THE SAINT LOUIS GATEWAY ARCH a Find the -intercepts. b. How wide is the Arch at its base? How do ou know? d. Draw a quick sketch of the Gatewa Arch. Label the aes with all the values ou know. and Find the -intercept. Use our calculated intercepts to re-set our WINDOW. Verif the intercepts of the Gatewa Arch from the graph. c. How tall is the Arch? How do ou know?

9 9.1.4 Which method should I use? Choosing a Strateg a. Strateg to tr first: Solve: b. Strateg to tr first: Solve: c. Strateg to tr first: Solve: d. Strateg to tr first: Solve:

10 e. Strateg to tr first: Solve: f. Strateg to tr first: Solve: Solution(s): Solution(s): Learning Log Choosing a Strateg to Solve Quadratics When should ou tr Factoring? When should ou tr Completing the Square? When should ou use the Quadratic Formula? When should ou Graph?

11 9-36. a. What is Stanton talking about? b. How can the equation be re-written? c. Solve our re-written equation from part b. Re-written equation: d. Use our graphing calculator s graph and table to check our solutions. Was Kle right? a. When is the o-o in Moe s hand? d. Draw a sketch of the graph representing the o-o s path. Label ke points. b. How long is the o-o going down before it starts coming back up? c. How far awa from Moe s hand is the o-o when it is at the farthest point awa from his hand?

12 9.2.1 What if the quantities are not equal? Solving Linear, One-Variable Inequalities a. 2 b c. 3 d e. 2 f g. 2 4 h a. b. c a. b. c. d SOLUTIONS TO A LINEAR INEQUALITY a. d. b/c Check a point in the shaded region to make sure it works in the original inequalit.

13 9-48. SOLVING LINEAR INEQUALITIES WITH ONE VARIABLE a/b/c b/c Check a point on each side of the boundar point to decide where the solutions are. Boundar Point: Should the boundar point be included? Find all the solutions for Check a point in the shaded region to make sure it works in the original inequalit How can I use inequalities? More Solving Inequalities a. 7 2 b. 3m 2 8m

14 c. 2 3 p 2 4 d e. 9k 4 1 2k 3 7k f THE UNITED NATIONS Answer in a sentence:

15 9-58. a. b. c What if the inequalit has two variables? Graphing Linear, Two-Variable Inequalities EXAMINING THE SOLUTIONS OF A LINEAR EQUATION Graph 2 3 a. Is 1,5 a solution to the equation? How can ou tell using the graph? How can ou tell using the equation? b. Is 2, 1 a solution to the equation? How about 0,0? c.

16 9-66. GRAPHING A LINEAR, TWO-VARIABLE INEQUALITY a. Class Activit for 2 3 b. Do ou suspect there are an points that are solutions, but don t have stickers? If so, where are the? Are there an stickers that ou think ma be misplaced? If so, where are the? What about the points ON the line? Are all points ON the line solutions? How man solutions are there? Where are there no stickers? Wh aren t there an stickers there? a. b a. Graph b. Graph 4 2

17 c. Graph d. Graph Learning Log Graphing Linear Inequalities How can ou determine if the line is part of the solution? How can ou determine which side of the line the solutions belong to? What point(s) is (are) easiest to test? How man points do ou need to test?

9.3.2 What if the inequalit is not linear? Graphing Linear and Non-Linear Inequalities 9-77. Graph 5 3 3 b. Wh is testing 0,0 convenient? c. Test 3,2.

18 9.3.2 What if the inequalit is not linear? Graphing Linear and Non-Linear Inequalities Graph b. Wh is testing 0,0 convenient? c. Test 3,2. Does this point help ou decide which side of the line to shade? Wh or wh not? a. What is the minimum number of points ou need to test to know which side of the line solutions are located? FOREIGN AID Use this graph to help answer parts a & b on the net page.

19 a. A constraint is: If = population and = # of people in povert, constraint: b. Which countries should receive foreign aid? Graph: Use Graphing Short-Cuts. (Use the table onl if necessar.) a. Graph

20 b. Graph c. Graph Graph 2 1

21 9.4.1 How can I represent it? Sstems of Inequalities a. Graph 5 Graph b. Graph the sstem: c. d.

22 9-90. Graph the sstem: HOW MANY REGIONS? a. b. c. d.

23 9-92. a b c How can I appl it? More Sstems of Inequalities Graph the sstem: 4 4 4

24 SEARCH AND RESCUE Constraints: a. Graph the sstem:

25 b. Graph the sstem: c. Graph the sstem: Learning Log Graphing Sstems of Inequalities

26 9.4.3 How can I use inequalities to solve problems? Appling Inequalities to Solve Problems UNITED NATIONS TO THE RESCUE Constraints:

27 a. How man food packages should the UN require from each countr? Eplain our answers. b. What is the largest number of medicine packages possible. What is the largest number of medicine packages that each countr can offer? Eplain EXTENSION How man food and medicine packages should each countr be required to send? Eplain.

9.1.1 What else can I solve?

CCA Ch 9: Solving Quadratics and Inequalities Name Team # 9.1.1 What else can I solve? Solving Quadratic Equations 9-1. USE THE ZERO PRODUCT PROPERTY TO SOLVE FOR X. a. 9 3 2 4 6 b. 0 3 5 2 3 c. 2 6 0