Lesson.1 Skills Practice Name Date Ladies and Gentlemen: Please Welcome the Quadratic Formula! The Quadratic Formula Vocabulary Complete the Quadratic Formula. Then, identify the discriminant and explain what it indicates about the function. The quadratic equation of the form ax 2 1 bx 1 c 5 0, can be written as the Quadratic Formula. x 5 Problem Set Determine the approximate zeros or roots of each function or equation. Round your answers to the nearest thousandth, if necessary. 1. f(x) 5 x 2 1 3x 2 5 a 5 1, b 5 3, c 5 25 2b 6 b x 5 2 2 4ac 2a x 5 2(3) 6 (3 ) 2 2 4(1)(25) 2(1) 23 6 29 2 23 1 5.385 23 6 9 1 20 x 5 2 x 5 x 5 2 or x 5 23 2 5.385 2 x 1.193 or x 24.193 2. f(x) 5 23 x 2 2 x 1 7 Chapter Skills Practice 951
Lesson.1 Skills Practice page 2 3. 2 x 2 1 6x 2 7 5 2 4. 4 x 2 2 x 2 1 5 5 5. f(x) 5 28 x 2 1 2x 1 1 6. 3 x 2 1 x 1 3 5 5 952 Chapter Skills Practice
Lesson.1 Skills Practice page 3 Name Date Determine the exact zeros or roots of each function or equation. 7. f(x) 5 22 x 2 2 8x 1 1 a 5 22, b 5 28, c 5 1 2b 6 b x 5 2 2 4ac 2a x 5 2(28) 6 (28 ) 2 2 4(22)(1) 2(22) x 5 8 6 72 24 x 5 8 6 36? 2 24 x 5 8 6 6 2 24 2 3 x 5 22 2 2 x 5 8 6 64 1 8 24 x 5 8 1 6 or x 5 8 2 6 2 24 24 3 2 or x 5 22 1 2 2 8. 5 x 2 1 8x 2 3 5 1 Chapter Skills Practice 953
Lesson.1 Skills Practice page 4 9. 23 x 2 1 6x 1 2 5 25 10. f(x) 5 x 2 1 6x 1 5 11. f(x) 5 22 x 2 1 5x 2 1 12. 23 x 2 1 8x 2 2 5 26 954 Chapter Skills Practice
Lesson.1 Skills Practice page 5 Name Date Use the discriminant to determine the number of zeros or roots each function or equation has. Then solve for the zeros or roots. 13. f(x) 5 2 x 2 1 6x 1 7 a 5 21, b 5 6, c 5 7 b 2 2 4ac 5 (6) 2 2 4(21)(7) 5 36 1 28 5 64 Because b 2 2 4ac. 0 the function has two zeros. 2b 6 b x 5 2 2 4ac 2a 2(6) 6 64 x 5 2(21) x 5 26 6 8 22 x 5 26 1 8 or x 5 26 2 8 22 22 x 5 2 or x 5 2 22 22 x 5 21 or x 5 7. 2 x 2 1 8x 1 3 5 25 15. f(x) 5 9 x 2 1 5x 1 1 Chapter Skills Practice 955
Lesson.1 Skills Practice page 6 16. 6 x 2 1 3x 2 5 5 2 17. f(x) 5 5 x 2 1 10x 1 5 18. f(x) 5 7 x 2 1 9x 1 5 956 Chapter Skills Practice
Lesson.2 Skills Practice Name Date It s Watching and Tracking! Using a Calculator-Based Ranger to Model Quadratic Motion Vocabulary Define each term in your own words. 1. quadratic regression 2. coefficient of determination Problem Set Use your graphing calculator to determine the quadratic regression equation and coefficient of determination for the line of best fit of each given data set. Determine if the equation is a good fit for the data. Round your answers to the nearest hundredth. 1. x y 0 0 1 4.05 2 5.50 3 6.25 4 3.50 5 0 y 5 20.97 x 2 1 4.84x 1 0.03 r 2 0.99 Because the r 2 value is close to 1, the quadratic regression equation is a good fit for the data. Chapter Skills Practice 957
Lesson.2 Skills Practice page 2 2. x y 0 2.1 0.5 3.4 1 4.1 1.5 4.3 2 3.9 2.5 2.3 3. x y 25 20.5 24 5 21 7 0 3 0.5 21 1 3 958 Chapter Skills Practice
Lesson.2 Skills Practice page 3 Name Date 4. x y 24 3.05 23 21.50 22 24.80 21 25.18 0 23.75 1 21.79 5. x y 0 6.2 1 4.5 2 1.5 3 20.5 4 2.4 5 3.9 Chapter Skills Practice 959
Lesson.2 Skills Practice page 4 6. x y 25 7.21 24 1.80 23 22.40 22 25.92 21 21.40 0 2.73 960 Chapter Skills Practice
Lesson.3 Skills Practice Name Date They re A Lot More than Just Sparklers! Solving Quadratic Inequalities Problem Set Determine the roots of each quadratic inequality. Use the interval method to determine the solution set of the inequality. Round your answer to the nearest thousandth if necessary. 1. x 2 2 7x 1 16 $ 10 x 2 2 7x 1 16 $ 10 x 2 2 7x 1 6 $ 0 x 2 2 7x 1 6 5 0 (x 2 6)(x 2 1) 5 0 x 2 6 5 0 or x 2 1 5 0 x 5 6 or x 5 1 Test 0, 2, and 7. x 2 2 7x 1 16 $ 10 (0 ) 2 2 7(0) 1 16 $ 10 16 $ 10 x 2 2 7x 1 16 $ 10 (2 ) 2 2 7(2) 1 16 $ 10 4 2 1 16 $ 10 6 $ 10 x 2 2 7x 1 16 $ 10 (7 ) 2 2 7(7) 1 16 $ 10 49 2 49 1 16 $ 10 16 $ 10 Solution: x e (2`, 1] or x e [6, `) Chapter Skills Practice 961
Lesson.3 Skills Practice page 2 2. x 2 1 7x 2 2, 212 3. x 2 1 x 2 15, 4 962 Chapter Skills Practice
Lesson.3 Skills Practice page 3 Name Date 4. 2 x 2 1 11x 2 21 # 2 5. 2 x 2 1 4x 2 5 # 22 Chapter Skills Practice 963
Lesson.3 Skills Practice page 4 6. 2 x 2 2 3x 1. 23 A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second. The quadratic function h(t) 5 216 t 2 1 35t 1 5 represents the height of the balloon, h, in feet t seconds after it is thrown. Use this information to answer each question. 7. How long does it take for the balloon to reach the ground? Round your answer to the nearest thousandth. 0 5 216 t 2 1 35t 1 5 a 5 216, b 5 35, c 5 5 2b 6 b t 5 2 2 4ac 2a 2(35) 6 (35 ) t 5 2 2 4(216)(5) 2(216) 235 6 1545 232 235 1 39.306 235 6 1225 1 320 t 5 232 t 5 t 5 232 or t 5 235 2 39.306 232 t < 20.1346 or t < 2.322 It will take just over 2.3 seconds for the balloon to reach the ground. 964 Chapter Skills Practice
Lesson.3 Skills Practice page 5 Name Date 8. Determine when the balloon is less than 10 feet above the ground. Round your answer to the nearest thousandth. 9. Determine when the balloon is more than 10 feet above the ground. Round your answer to the nearest thousandth. Chapter Skills Practice 965
Lesson.3 Skills Practice page 6 10. Determine when the balloon is less than 20 feet above the ground. Round your answer to the nearest thousandth. 11. Determine when the balloon is more than 20 feet above the ground. Round your answer to the nearest thousandth. 966 Chapter Skills Practice
Lesson.3 Skills Practice page 7 Name Date 12. Determine when the balloon is less than 30 feet above the ground. Round your answer to the nearest thousandth. Chapter Skills Practice 967
968 Chapter Skills Practice
Lesson.4 Skills Practice Name Date You Must Have a System Systems of Quadratic Equations Problem Set Solve each system of equations algebraically. Then verify each solution graphically. 1. y 5 x 2 2 6x 1 7 y 5 2x 2. y 5 x 2 2 3x 1 1 y 5 x 2 3 y (7, ) 12 10 8 6 4 2 (1, 2) 28 26 24 22 0 2 4 6 8 x 22 2x 5 x 2 2 6x 1 7 0 5 x 2 2 8x 1 7 0 5 (x 2 7)(x 2 1) x 2 7 5 0 or x 2 1 5 0 x 5 7 x 5 1 y 5 2(7) y 5 2(1) y 5 y 5 2 The system has two solutions: (7, ) and (1, 2). Chapter Skills Practice 969
Lesson.4 Skills Practice page 2 3. y 5 2x 2 1 16x 1 24 4. y 5 2x 2 2 y 5 2x 2 1 6x 2 6 y 5 3x 1 1 970 Chapter Skills Practice
Lesson.4 Skills Practice page 3 Name Date 5. y 5 4x 2 1 6x 1 3 6. y 5 26x 2 6 y 5 3x 2 1 24x 1 50 y 5 4x 1 1 Chapter Skills Practice 971
Lesson.4 Skills Practice page 4 Solve each system of equations algebraically. Then verify each solution graphically. 7. y 5 x 2 2 2x 1 1 y 5 2 x 2 1 3x 1 4 y 2 x 2 1 3x 1 4 5 x 2 2 2x 1 1 0 5 2 x 2 2 5x 2 3 28 26 1 1 2, 2 2 4 24 8. y 5 2 x 2 2 x 1 3 y 5 x 2 1 5x 2 6 8 6 4 22 0 2 4 22 24 26 28 (3, 4) 6 8 x 0 5 (2x 1 1)(x 2 3) 2x 1 1 5 0 2x 5 21 1 x 5 2 2 y 5 ( 1 2 2 ) 2 2 2 ( 1 2 1 2 ) 1 1 x 2 3 5 0 y 5 4 1 1 1 1 x 5 3 5 2 1 y 5 9 4 or 4 y 5 (3 ) 2 2 2(3) 1 1 The system has two solutions: ( 2 1 2 y 5 9 2 6 1 1 y 5 4, 2 1 4 ) and (3, 4). 972 Chapter Skills Practice
Lesson.4 Skills Practice page 5 Name Date 9. y 5 x 2 2 4x 1 7 y 5 2 x 2 2 6x 2 11 10. y 5 2 x 2 1 4x 2 7 y 5 x 2 1 2x 1 1 Chapter Skills Practice 973
Lesson.4 Skills Practice page 6 11. y 5 x 2 2 8x 1 17 y 5 2x 2 1 6x 2 10 12. y 5 2x 2 2 3x 1 2 y 5 22x 2 1 x 1 1 974 Chapter Skills Practice