Page 1 Section 1.4 Quadratic Equations 33 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. Section 1.4 Quadratic Equations Objective: In this lesson you learned how to solve quadratic equations. I. Factoring (Page 109) To use the Zero-Factor Property to solve a quadratic equation, . . . aaaaa aaa aaaa aaaa aa aaa aaaaaaa aaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aa aaa aaaaaa aaaaaaaa aaaa aaaa aaa aaaaaaaaa aa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aaaaaa aaaaaa aaaaa aa aaaaa Example 1: Solve 27 12 2 - = - x x by factoring. aaa aaaaaaaaa aaa a aaa aa II. Extracting Square Roots (Page 110) Solving an equation of the form d u = 2 without going through the steps of factoring is called aaaaaaaaaa aaaa aaaaa . The equation d u = 2 , where d > 0, has exactly two solutions: u = a a and u = a a a . These solutions can also be written as u = a a a . Example 2: Solve 45 ) 4 ( 5 2 = - x by extracting square roots. aaa aaaaaaaaa aaa a aaa aa Course Number Instructor Date Important Vocabulary Define each term or concept. Quadratic equation aa aaaaaaaa aa a aaaa aaa aa aaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a a aaaaa aa aa aaa a aaa aaaa aaaaaaa aaaa a a aa Quadratic formula aaa aaaaaaaa a a aa a a a a a a aaa a a aaaa aaa aaaaaaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a aa Discriminant aaa aaaaaaaa aaaaa aaa aaaaaaa aaaaa a a a aaaa aa aaa aaaaaaaaa aaaaaaaa What you should learn How to solve quadratic equations by factoring What you should learn How to solve quadratic equations by extracting square roots Page 2 Section 1.4 Quadratic Equations 33 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. Section 1.4 Quadratic Equations Objective: In this lesson you learned how to solve quadratic equations. I. Factoring (Page 109) To use the Zero-Factor Property to solve a quadratic equation, . . . aaaaa aaa aaaa aaaa aa aaa aaaaaaa aaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aa aaa aaaaaa aaaaaaaa aaaa aaaa aaa aaaaaaaaa aa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aaaaaa aaaaaa aaaaa aa aaaaa Example 1: Solve 27 12 2 - = - x x by factoring. aaa aaaaaaaaa aaa a aaa aa II. Extracting Square Roots (Page 110) Solving an equation of the form d u = 2 without going through the steps of factoring is called aaaaaaaaaa aaaa aaaaa . The equation d u = 2 , where d > 0, has exactly two solutions: u = a a and u = a a a . These solutions can also be written as u = a a a . Example 2: Solve 45 ) 4 ( 5 2 = - x by extracting square roots. aaa aaaaaaaaa aaa a aaa aa Course Number Instructor Date Important Vocabulary Define each term or concept. Quadratic equation aa aaaaaaaa aa a aaaa aaa aa aaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a a aaaaa aa aa aaa a aaa aaaa aaaaaaa aaaa a a aa Quadratic formula aaa aaaaaaaa a a aa a a a a a a aaa a a aaaa aaa aaaaaaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a aa Discriminant aaa aaaaaaaa aaaaa aaa aaaaaaa aaaaa a a a aaaa aa aaa aaaaaaaaa aaaaaaaa What you should learn How to solve quadratic equations by factoring What you should learn How to solve quadratic equations by extracting square roots 34 Chapter 1 Equations and Inequalities Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. III. Completing the Square (Page 111) To complete the square for the expression bx x + 2 , add aaaaa a , which is the square of half the coefficient of x. When solving quadratic equations by completing the square, you must add this term to aaaa aaaa in order to maintain equality. The completing the square method can be used to solve a quadratic equation when . . . aaa aaaaaaaa aa aaa aaaaaaaaaaa When completing the square to solve a quadratic equation, if the leading coefficient is not 1, . . . aaa aaaa aaaaaa aaaa aaaa aa aaa aaaaaaaa aa aaa aaaaaaa aaaaaaaaaaa aaaaaa aaaaaaaaaa aaa aaaaaaa Example 3: Solve 0 8 10 2 = - + x x by completing the square. aaaaaaa aa aaa aaaaaaa aaaaaaa aaa aaaaaaaaa aaa a aaaaa aaa aaaaa IV. The Quadratic Formula (Pages 112-113) The verbal statement of the Quadratic Formula is . . . aaaaaaaaa aa aaaa aa aaaaa aaa aaaaaa aaaa aa a aaaaaaa aaaaa aaaa aaa aaaaaaa aa aaaa When using the Quadratic Formula, remember that before the formula can be applied, . . . aaa aaaa aaaaa aaaaa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aa a a aa aa a aa Example 4: For the quadratic equation 2 2 3 16 x x - = - , find the values of a, b, and c to be substituted into the Quadratic Formula. a a aa a a a aa aaa a a aaa aa a a a aa a a aa aaa a a a aa The discriminant of the quadratic expression c bx ax + + 2 can be used to . . . aaaaaaaaa aaa aaaaaa aa aaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaaa What you should learn How to solve quadratic equations by completing the square What you should learn How to use the Quadratic Formula to solve quadratic equations Page 3 Section 1.4 Quadratic Equations 33 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. Section 1.4 Quadratic Equations Objective: In this lesson you learned how to solve quadratic equations. I. Factoring (Page 109) To use the Zero-Factor Property to solve a quadratic equation, . . . aaaaa aaa aaaa aaaa aa aaa aaaaaaa aaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aa aaa aaaaaa aaaaaaaa aaaa aaaa aaa aaaaaaaaa aa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aaaaaa aaaaaa aaaaa aa aaaaa Example 1: Solve 27 12 2 - = - x x by factoring. aaa aaaaaaaaa aaa a aaa aa II. Extracting Square Roots (Page 110) Solving an equation of the form d u = 2 without going through the steps of factoring is called aaaaaaaaaa aaaa aaaaa . The equation d u = 2 , where d > 0, has exactly two solutions: u = a a and u = a a a . These solutions can also be written as u = a a a . Example 2: Solve 45 ) 4 ( 5 2 = - x by extracting square roots. aaa aaaaaaaaa aaa a aaa aa Course Number Instructor Date Important Vocabulary Define each term or concept. Quadratic equation aa aaaaaaaa aa a aaaa aaa aa aaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a a aaaaa aa aa aaa a aaa aaaa aaaaaaa aaaa a a aa Quadratic formula aaa aaaaaaaa a a aa a a a a a a aaa a a aaaa aaa aaaaaaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a aa Discriminant aaa aaaaaaaa aaaaa aaa aaaaaaa aaaaa a a a aaaa aa aaa aaaaaaaaa aaaaaaaa What you should learn How to solve quadratic equations by factoring What you should learn How to solve quadratic equations by extracting square roots 34 Chapter 1 Equations and Inequalities Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. III. Completing the Square (Page 111) To complete the square for the expression bx x + 2 , add aaaaa a , which is the square of half the coefficient of x. When solving quadratic equations by completing the square, you must add this term to aaaa aaaa in order to maintain equality. The completing the square method can be used to solve a quadratic equation when . . . aaa aaaaaaaa aa aaa aaaaaaaaaaa When completing the square to solve a quadratic equation, if the leading coefficient is not 1, . . . aaa aaaa aaaaaa aaaa aaaa aa aaa aaaaaaaa aa aaa aaaaaaa aaaaaaaaaaa aaaaaa aaaaaaaaaa aaa aaaaaaa Example 3: Solve 0 8 10 2 = - + x x by completing the square. aaaaaaa aa aaa aaaaaaa aaaaaaa aaa aaaaaaaaa aaa a aaaaa aaa aaaaa IV. The Quadratic Formula (Pages 112-113) The verbal statement of the Quadratic Formula is . . . aaaaaaaaa aa aaaa aa aaaaa aaa aaaaaa aaaa aa a aaaaaaa aaaaa aaaa aaa aaaaaaa aa aaaa When using the Quadratic Formula, remember that before the formula can be applied, . . . aaa aaaa aaaaa aaaaa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aa a a aa aa a aa Example 4: For the quadratic equation 2 2 3 16 x x - = - , find the values of a, b, and c to be substituted into the Quadratic Formula. a a aa a a a aa aaa a a aaa aa a a a aa a a aa aaa a a a aa The discriminant of the quadratic expression c bx ax + + 2 can be used to . . . aaaaaaaaa aaa aaaaaa aa aaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaaa What you should learn How to solve quadratic equations by completing the square What you should learn How to use the Quadratic Formula to solve quadratic equations Section 1.4 Quadratic Equations 35 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. If the discriminant ac b 4 2 - of the quadratic equation 0 2 = + + c bx ax , 0 ? a , is: 1) positive, then the quadratic equation . . . aaa aaa aaaaaaaa aaaa aaaaaaaaa aaa aaa aaaaa aaa aaa aaaaaaaaaaaaa 2) zero, then the quadratic equation . . . aaa aaa aaaaaaaa aaaa aaaaaaaa aaa aaa aaaaa aaa aaa aaaaaaaaaaaa 3) negative, then the quadratic equation . . . aaa aa aaaa aaaaaaaaa aaa aaa aaaaa aaa aa aaaaaaaaaaaa Example 5: Use the discriminant to find the number and type of solutions of the quadratic equation 0 18 5 6 2 = + - x x . aa aaaa aaaaaaaaa V. Applications of Quadratic Equations (Pages 114-117) Describe two real -life situations in which quadratic equations often occur. aaaaaaa aaaa aaaaa aaaaaaaa aaaaaaaaa aaaaaaa aaaaaaaa aaaaaaa aaaa aaaa aaa aaaaaaaa aaaaaaa aaaa aaa aaaaaaaaaa aa a aaaaa aaaaaaaaa The position equation giving the height of an object above the Earthâ€™s surface is a a a aaa a aa a a a a a , where . . . a aaaaaaaaaa aaa aaaaaa aa aaa aaaaaa aa aaaaa a a aaaaaaaaaa aaa aaaaaaa aaaaaaaa aa aaa aaaaaa aa aaaa aaa aaaaaaa a a aaaaaaaaaa aaa aaaaaaa aaaaaa aa aaa aaaaaa aa aaaaa aaa a aaaaaaaaaa aaaa aa aaaaaaaa Homework Assignment Page(s) Exercises What you should learn How to use quadratic equations to model and solve real -life problems Page 4 Section 1.4 Quadratic Equations 33 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. Section 1.4 Quadratic Equations Objective: In this lesson you learned how to solve quadratic equations. I. Factoring (Page 109) To use the Zero-Factor Property to solve a quadratic equation, . . . aaaaa aaa aaaa aaaa aa aaa aaaaaaa aaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aa aaa aaaaaa aaaaaaaa aaaa aaaa aaa aaaaaaaaa aa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aaaaaa aaaaaa aaaaa aa aaaaa Example 1: Solve 27 12 2 - = - x x by factoring. aaa aaaaaaaaa aaa a aaa aa II. Extracting Square Roots (Page 110) Solving an equation of the form d u = 2 without going through the steps of factoring is called aaaaaaaaaa aaaa aaaaa . The equation d u = 2 , where d > 0, has exactly two solutions: u = a a and u = a a a . These solutions can also be written as u = a a a . Example 2: Solve 45 ) 4 ( 5 2 = - x by extracting square roots. aaa aaaaaaaaa aaa a aaa aa Course Number Instructor Date Important Vocabulary Define each term or concept. Quadratic equation aa aaaaaaaa aa a aaaa aaa aa aaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a a aaaaa aa aa aaa a aaa aaaa aaaaaaa aaaa a a aa Quadratic formula aaa aaaaaaaa a a aa a a a a a a aaa a a aaaa aaa aaaaaaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaa aa aaa aaaaaaa aaaa aa a a aa a a a aa Discriminant aaa aaaaaaaa aaaaa aaa aaaaaaa aaaaa a a a aaaa aa aaa aaaaaaaaa aaaaaaaa What you should learn How to solve quadratic equations by factoring What you should learn How to solve quadratic equations by extracting square roots 34 Chapter 1 Equations and Inequalities Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. III. Completing the Square (Page 111) To complete the square for the expression bx x + 2 , add aaaaa a , which is the square of half the coefficient of x. When solving quadratic equations by completing the square, you must add this term to aaaa aaaa in order to maintain equality. The completing the square method can be used to solve a quadratic equation when . . . aaa aaaaaaaa aa aaa aaaaaaaaaaa When completing the square to solve a quadratic equation, if the leading coefficient is not 1, . . . aaa aaaa aaaaaa aaaa aaaa aa aaa aaaaaaaa aa aaa aaaaaaa aaaaaaaaaaa aaaaaa aaaaaaaaaa aaa aaaaaaa Example 3: Solve 0 8 10 2 = - + x x by completing the square. aaaaaaa aa aaa aaaaaaa aaaaaaa aaa aaaaaaaaa aaa a aaaaa aaa aaaaa IV. The Quadratic Formula (Pages 112-113) The verbal statement of the Quadratic Formula is . . . aaaaaaaaa aa aaaa aa aaaaa aaa aaaaaa aaaa aa a aaaaaaa aaaaa aaaa aaa aaaaaaa aa aaaa When using the Quadratic Formula, remember that before the formula can be applied, . . . aaa aaaa aaaaa aaaaa aaa aaaaaaaaa aaaaaaaa aa aaaaaaa aaaa aa a a aa aa a aa Example 4: For the quadratic equation 2 2 3 16 x x - = - , find the values of a, b, and c to be substituted into the Quadratic Formula. a a aa a a a aa aaa a a aaa aa a a a aa a a aa aaa a a a aa The discriminant of the quadratic expression c bx ax + + 2 can be used to . . . aaaaaaaaa aaa aaaaaa aa aaa aaaaaaaaa aa a aaaaaaaaa aaaaaaaaa What you should learn How to solve quadratic equations by completing the square What you should learn How to use the Quadratic Formula to solve quadratic equations Section 1.4 Quadratic Equations 35 Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved. If the discriminant ac b 4 2 - of the quadratic equation 0 2 = + + c bx ax , 0 ? a , is: 1) positive, then the quadratic equation . . . aaa aaa aaaaaaaa aaaa aaaaaaaaa aaa aaa aaaaa aaa aaa aaaaaaaaaaaaa 2) zero, then the quadratic equation . . . aaa aaa aaaaaaaa aaaa aaaaaaaa aaa aaa aaaaa aaa aaa aaaaaaaaaaaa 3) negative, then the quadratic equation . . . aaa aa aaaa aaaaaaaaa aaa aaa aaaaa aaa aa aaaaaaaaaaaa Example 5: Use the discriminant to find the number and type of solutions of the quadratic equation 0 18 5 6 2 = + - x x . aa aaaa aaaaaaaaa V. Applications of Quadratic Equations (Pages 114-117) Describe two real -life situations in which quadratic equations often occur. aaaaaaa aaaa aaaaa aaaaaaaa aaaaaaaaa aaaaaaa aaaaaaaa aaaaaaa aaaa aaaa aaa aaaaaaaa aaaaaaa aaaa aaa aaaaaaaaaa aa a aaaaa aaaaaaaaa The position equation giving the height of an object above the Earthâ€™s surface is a a a aaa a aa a a a a a , where . . . a aaaaaaaaaa aaa aaaaaa aa aaa aaaaaa aa aaaaa a a aaaaaaaaaa aaa aaaaaaa aaaaaaaa aa aaa aaaaaa aa aaaa aaa aaaaaaa a a aaaaaaaaaa aaa aaaaaaa aaaaaa aa aaa aaaaaa aa aaaaa aaa a aaaaaaaaaa aaaa aa aaaaaaaa Homework Assignment Page(s) Exercises What you should learn How to use quadratic equations to model and solve real -life problems 36 Chapter 1 Equations and Inequalities Larson/Hostetler Algebra and Trigonometry, Sixth Edition Student Success Organizer Copyright © Houghton Mifflin Company. All rights reserved.Read More

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