5 Section 9.1 Prop of Radicals. 7 Section Section 9. 1b Properties of Radicals. 8 Quick Quiz Section 9.4 Completing the Square
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1 Unit 10B Quadratics - Chapter 9 Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and make any necessary changes. All assignments are due the following class period unless indicated otherwise. Monday Tuesday Wednesday Thursday Friday 4 MapTesting 7 Section Section 9.1 Prop of Radicals 6 Section 9. 1b Properties of Radicals 8 Quick Quiz Section 9.4 Completing the Square 11 Section 9.4b 18 1 Section9.4c/ 9.5a Quadratic Formula Section 9.5 b c 15 Review Quadratics Review Quadratics Test on Solving Quadratics Section Page Assignment 9.1 p b p p p b 9.5a p b Chapter 9 Review 1
2 Lesson 9.1 Properties of Radicals Algebra 1 Essential Question How can you multiply and divide square roots? 1 EXPLORATION: Operations with Square Roots For each operation with square roots, compare the results obtained using the two indicated orders of operations. What can you conclude? a. Square Roots and Multiplication Is 4 9equal to 4 9? In general, is a b equal to a b? Explain your reasoning. b. Square Roots and Division Is equal to In general, is a b a equal to? b Explain your reasoning. Core Concepts Product Property of Square Roots Words The square root of a product equals the product of the square roots of the factors. Numbers Algebra ab a b, where a, b 1. Simplifying Radicals with the Product Property Simplify each radical into its simplest form. (a) 50 (b) 15 (c) 48 (d) 300 (e) 7 (f) 18 (g) 88
3 Quotient Property of Square Roots Words The square root of a quotient equals the quotient of the square roots of the numerator and denominator. Numbers a a Algebra, where a and b 4 4 b b. Simplifying Radicals with the Quotient Property Simplify each radical into its simplest form (a) (b) (c) (d) (e) Simplify each radical into its simplest form. 6 (a) 16g (b) 51h (c) (d) 4 r 49x 64y 3 Lesson 9.1 Properties of Radicals Day Algebra 1 A radical is simplest form when 3 conditions are met: No radicands have No radicands contain No radicals appear in the 3
4 1. Dividing Radicals (Rationalizing the Denominator) Simplify the Radical 5 7 (a) (b) (c) (d) 4 3 (e) b 4 a b (f) Practice Dividing Radicals
5 Lesson 9.1 Worksheet Name I. Simplify each expression completely
6 Lesson 9.3 Solving Quadratic Equations Using Square Roots Algebra 1 Essential Question How can you determine the number of solutions of a quadratic equation of the form ax + c = 0? 1. Finding Square Roots Evaluate. (a) 81 (b) 100 (c) 64 (d) 9. What is the square root of 36? 3. Solving Quadratics Equations in the Form: Solve the following quadratic equations. x c (a) x 81 (b) x 17 (c) x 5 4. Solving Quadratics Equations in the Form: Solve the following quadratic equations. ax c (a) x 1 (b) x 1 (c) 3x 7 (d) 1x 60 ( e) x 196 (f) x
7 5. Application Exercise Falling Object Model You have entered Mr. Esbrook s first annual egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 3 feet without breaking the egg. In you quest to become egg-dropping champion, you have asked your Algebra class to determine the time it will take for the egg container to hit the ground. About how long will it take for the egg s container to hit the ground? Assume there is no air Algebra: Section 9.1/ 9.3 Worksheet Name Date Hour Solve each equation using square roots. Simplify square roots if necessary. There should be no decimal answers. 1. x = 100. y = 3 3. ¼ a = x = y + 14 = b 6 = 9 7. ½ x 7 = 1 8. x + 5 = x + 6 = x = x x 3 5 7
8 simplify Find the area of a square with side length 0. Find the area of a triangle with height and base. 1. Using the Falling Object Model found in section 9.1. Determine approximately how long it will take a I- phone to hit the ground when dropped from a window 5 feet above the ground. Lesson 9.4(a) Completing the Square (w/ Leading Coefficient 1) Algebra 1 1. Completing the Square Complete the square so that each expression is a perfect square trinomial. Then factor the trinomial. (a) x 1x (b) x 8x (c) x 30x Completing the Square To complete the square for any quadratic expression in the form add of the second coefficient (b) to the end. 8
9 . Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square. (a) x 10x 4 (b) x 6x 7 (c) 1 x x 4 (d) x x 3 Lesson 1.4(b) Completing the Square (w/ Leading Coefficient 1) Algebra 1 Warm-Up Exercise Solve by Completing the Square. (a) x x 14 (b) x 4x 1 7 Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square. 1. x 8x x 4x 8 9
10 3. 3x 6x 4. 10x 13x x 6x x 8x In Exercises 7-1, determine whether the quadratic function has a maximum or minimum value. Then find the value. 7. y x 4x 3 8. y x 6x y x 8x 10. y x 10x y x x y x x
11 13. Choosing a Method to Solve a Quadratic Determine the easiest method to solve the quadratics below. Tell which method you used, and then solve the equation. (a) 5 x 40 (b) x 5x 6 (c) x 8x 5 5 Lesson 9.5(a) The Quadratic Formula Algebra 1 Essential Question How can you derive a formula that can be used to write the solutions of any quadratic equation in standard form? The following steps show a method of solving ax bx c. Explain what was done in each step. ax bx c 0 1. Write the equation. 4a x 4abx 4ac. 4a x 4abx 4ac b b 3. 4a x 4abx b b 4ac 4. ax b b 4ac 5. ax b b 4ac 6. ax b b 4ac 7. Quadratic Formula: x a b b 4ac 8. 11
12 Core Concepts Quadratic Formula The real solutions of the quadratic equation ax bx c are x a b b 4ac Quadratic Formula where a and b 4ac. Interpreting the Discriminant b 4ac b 4ac b 4ac Methods for Solving Quadratic Equations Method Advantages Disadvantages Factoring (Lessons ) Graphing (Lesson 9.) Using Square Roots (Lesson 9.3) Completing the Square (Lesson 9.4) Quadratic Formula (Lesson 9.5) Practice In Exercises 1 6, solve the equation using the Quadratic Formula. 1. x 10x 16. x x x x 1
13 4. x 6x x 5x x 8x A square pool has a side length of x feet. A uniform border around the pool is 1 foot wide. The total area of the pool and the border is 361 square feet. What is the area of the pool? In Exercises 8 10, determine the number of real solutions of the equation. 8. x 6x 3 9. x 6x x 3x 8 In Exercises find the number of x-intercepts of the graph of the function. 11. y x 4x 3 1. y x 14x y x 8x 18 In Exercises 14 16, solve the equation using any method. Explain your choice of method. 14. x 4x x 8x x x 5 13
14 Lesson 9.5(b) Worksheet The Quadratic Formula 1. Recite the Quadratic Formula. Name x = Solve each quadratic equation by using the Quadratic Formula. You must solve by using the Quadratic Formula. No other method will be accepted.. x 5x x 11x x x 5. x x 8 6. x 3x 1 7. x 7x 3 8. x x x x 10. 3x 3x 6 14
15 11. 5x 14x x 11x x 10x x x x 10x 5 Lesson Review Worksheet Name Algebra 1 I. Using the Discriminant Find the discriminant of each quadratic equation and give the number and type of the solutions of the equation. 1. x 5x 11. x 5x 7 3. x 5 10x 4. 6x 5 x 5. 1x 5 II. Solving Quadratic Equations by Using the Quadratic Formula Use the Quadratic Formula to solve each of the quadratic equations below. Be sure to simplify your solutions x 8x x x x 4x 15
16 9. x x x 5 4x 11. 6x 3 8x III. Solving Quadratic Equations by Completing the Square Solve each of the quadratic equations below by Completing the Square. Be sure to simplify your solutions. 1. x 4x x 16x x 30x 66 IV. Solving Quadratic Equations by Choosing a Method Solve each of the quadratic equations below by any method (Complete the Square, Factoring, Square Roots, or Quadratic Formula) 15. x 8x x 9x 17. 6x 3x x 5x x x 10 16
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