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Lesson 3 Menu

Five-Minute Check (over Lesson 9-2) Main Ideas and Vocabulary Targeted TEKS Example 1: Irrational Roots Key Concept: Completing the Square Example 2: Complete the Square Example 3: Solve an Equation by Completing the Square Example 4: Solve a Quadratic Equation in Which a ≠ 1.

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Lesson 3 Menu

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  1. Five-Minute Check (over Lesson 9-2) Main Ideas and Vocabulary Targeted TEKS Example 1: Irrational Roots Key Concept: Completing the Square Example 2: Complete the Square Example 3: Solve an Equation by Completing theSquare Example 4: Solve a Quadratic Equation in Which a≠ 1 Lesson 3 Menu

  2. Solve quadratic equations by finding the square root. • Solve quadratic equations by completing the square. • completing the square Lesson 3 MI/Vocab

  3. Irrational Roots Solve x2 + 6x + 9 = 5 by taking the square root of each side. Round to the nearest tenth if necessary. x2 + 6x + 9 = 5 Original equation (x + 3)2 = 5 x2 + 6x + 9 is a perfect square trinomial. Take the square root of each side. Take the square root of each side. Definition of absolute value Lesson 3 Ex1

  4. or Irrational Roots Subtract 3 from each side. Simplify. Use a calculator to evaluate each value of x. Answer: The solution set is {–5.2, –0.8}. Lesson 3 Ex1

  5. Solve x2 + 8x + 16 = 3 by taking the square root of each side. Round to the nearest tenth if necessary. • A • B • C • D A. {–4} B. {–2.3, –5.7} C. {2.3, 5.7} D.Ø Lesson 3 CYP1

  6. Key Concept 9-3

  7. To make the figure a square, add 36 positive 1-tiles. Arrange the tiles for x2 – 12x + c so that the two sides of the figure are congruent. Complete the Square Find the value of c that makes x2 – 12x + c a perfect square. Method 1 Use algebra tiles. x2 – 12x +36 is a perfect square. Lesson 3 Ex2

  8. Step 1 Complete the Square Method 2 Complete the square. Step 2 Square the result (–6)2 = 36 of Step 1. Step 3 Add the result of x2 –12x + 36 Step 2 to x2 – 12x. Answer:c = 36 Notice that x2 – 12x + 36 = (x – 6)2. Animation: Completing the Square Lesson 3 Ex2

  9. Find the value of c that makes x2 + 14x + c a perfect square. • A • B • C • D A. 7 B. 14 C. 156 D. 49 Lesson 3 CYP2

  10. x2 – 18x + 81 = –17 + 81 Solve an Equation by Completing the Square Solve x2 – 18x + 5 = –12 by completing the square. Isolate the x2 and x terms. Then complete the square and solve. x2 – 18x + 5 = –12 Original equation x2 + 18x – 5 – 5 = –12 – 5 Subtract 5 from each side. x2 – 18x = –17 Simplify. Lesson 3 Ex3

  11. Solve an Equation by Completing the Square (x – 9)2 = 64 Factor x2 –18x + 81. (x – 9) = ±8 Take the square root of each side. x – 9 + 9 = ±8 + 9 Add 9 to each side. x = 9 ± 8 Simplify. x = 9 + 8 or x = 9 – 8 Separate the solutions. = 17 = 1 Simplify. Answer: The solution set is {1, 17}. Lesson 3 Ex3

  12. Solve x2 – 8x + 10 = 30. • A • B • C • D A. {–2, 10} B. {2, –10} C. {2, 10} D.Ø Lesson 3 CYP3

  13. Solve a Quadratic Equation in Which a≠ 1 CANOEING Suppose the rate of flow of an 80-foot-wide river is given by the equationr = –0.01x2 + 0.8x where r is the rate in miles per hour, and x is the distance from the shore in feet. Joacquim does not want to paddle his canoe against a current faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour? ExploreYou know the function that relates distance from shore to the rate of the river current. You want to know how far away from the river bank he must paddle to avoid the current. Lesson 3 Ex4

  14. Solve a Quadratic Equation in Which a≠ 1 Plan Find the distance when r = 5. Use completing the square to solve –0.01x2 + 0.8x = 5. Solve–0.01x2 + 0.8x = 5 Equation for the current Divide each side by –0.01. x2 – 80x = –500 Simplify. Lesson 3 Ex4

  15. Take the square root of each side. Add 40 to each side. Simplify. Solve a Quadratic Equation in Which a≠ 1 x2 – 80x+ 1600 = –500 + 1600 (x – 40)2 = 110 Factor x2 – 80x + 1600. Lesson 3 Ex4

  16. Solve a Quadratic Equation in Which a≠ 1 Use a calculator to evaluate each value of x. Examine The solutions of the equation are about 7 ft and about 73 ft. The solutions are distances from one shore. Since the river is about 80 ft wide, 80 – 73 = 7. Answer:He must stay within about 7 feet of either bank. Lesson 3 Ex4

  17. BOATINGSuppose the rate of flow of a 60-foot-wide river is given by the equation r = –0.01x2 + 0.6x where r is the rate in miles per hour, and x is the distance from the shore in feet. Joacquimdoes not want to paddlehis canoe against a current faster than 5 miles per hour.At what distance from the river bank must he paddlein order to avoid a current of 5 miles perhour? • A • B • C • D A. 6 feet B. 5 feet C. 1 foot D. 10 feet Lesson 3 CYP4

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