 # 9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 1. 3x +(– 6x) Warm-Up.

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9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 1. 3x +(– 6x) Warm-Up Simplify the expression. 2. 5 + 4x + 2 –3 x ANSWER 4x + 7 ANSWER 3. 4(2x – 1) + x 9x – 4 ANSWER 4. – (x + 4) – 6 x – 7x – 4 ANSWER

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Warm-Up Simplify the expression. 13. (x 5 ) 3 14. (– x) 3 11. (3xy) 3 27x 3 y 3 ANSWER 12. xy 2 xy 3 x2y5x2y5 ANSWER x 15 ANSWER –x3–x3

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root.

Find the two square roots of each number. 7 is a square root, since 7 7 = 49. –7 is also a square root, since –7 –7 = 49. 10 is a square root, since 10 10 = 100. –10 is also a square root, since –10 –10 = 100. 49 = –7 – 49 = 7 100 = 10 100 = –10 – A. 49 B. 100 C. 225 15 is a square root, since 15 15 = 225. 225 = 15 225 = –15 – –15 is also a square root, since –15 –15 = 225.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. A. 25 Check It Out: Example 1 5 is a square root, since 5 5 = 25. –5 is also a square root, since –5 –5 = 25. 12 is a square root, since 12 12 = 144. –12 is also a square root, since –12 –12 = 144. 25 = –5 – 25 = 5 144 = 12 144 = –12 – Find the two square roots of each number. B. 144 C. 289 289 = 17 289 = –17 – 17 is a square root, since 17 17 = 289. –17 is also a square root, since –17 –17 = 289.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Additional Example 3A: Evaluating Expressions Involving Square Roots Simplify the expression. Evaluate the square root. Add. = 25 Multiply. = 18 + 7 3 36 + 7 3 36 + 7 = 3(6) + 7

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Additional Example 3B: Evaluating Expressions Involving Square Roots Simplify the expression. + 25 16 3434 3434 + 3434 = + 1.5625 Evaluate the square roots. = 1.25 + 3434 25 16 = 1.5625. = 2 Add.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Check It Out: Example 3A Simplify the expression. Evaluate the square root. Add.= 14 Multiply.= 10 + 4 2 25 + 4 2 25 + 4 = 2(5) + 4

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Check It Out: Example 3B Simplify the expression. + 18 t2 1414 1414 + 1414 = + 9 Evaluate the square roots. = 3 + 1414 18 t2 = 9. = 3 Add. 1414

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 3. Evaluate the expression. A. 17 B. 17 C. 19 D. 72 Lesson Quiz for Student Response Systems

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. 4. Evaluate the expression. A. 4 B. 8 C. 16 D. 40 Lesson Quiz for Student Response Systems

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. A Quadratic equation is an equation that can be written in the following standard form: ax 2 + bx + c = 0 where a does not equal 0 If b = 0 ax 2 + c = 0 These are the type we will work with today. If b = 0 and c = 0 ax 2 = 0

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solving Quadratic Equations a.x 2 = 4 b.x 2 = 5 c.x 2 = 0 d.x 2 = -1

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solving Quadratic Equations a.x 2 = 25 b.x 2 = 7 c.x 2 = 81 d.x 2 = -12

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ± 4 = ± 2  Take square roots of each side. Simplify. ANSWER The solutions are – 2 and 2.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 1 b. m 2 – 18 = – 18 Write original equation. m 2 = 0 Add 18 to each side.. The square root of 0 is 0. m = 0m = 0 ANSWER The solution is 0.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 1 c. b 2 + 12 = 5 Write original equation. b 2 = – 7 Subtract 12 from each side. ANSWER Negative real numbers do not have real square roots. So, there is no solution.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve quadratic equations Solve the equation. 1. c 2 – 25 = 0 SOLUTION c 2 – 25 = 0 Write original equation. c = ± 25 = ± 5  Take square roots of each side. Simplify. GUIDED PRACTICE ANSWER The solutions are – 5 and 5.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 2 Take square roots of a fraction Solve 4z 2 = 9. SOLUTION 4z 2 = 9. Write original equation. z 2 = 9 4 Divide each side by 4. Take square roots of each side. z = ±  9 4 3 2 Simplify. ANSWER The solutions are – and 3 2 3 2

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Approximate solutions of a quadratic equation Solve 3x 2 – 11 = 7. Round the solutions to the nearest hundredth. SOLUTION 3x 2 – 11 = 7 Write original equation. 3x 2 = 18 Add 11 to each side. x 2 = 6 Divide each side by 3. x = ± 6  Take square roots of each side. x ± 2.45 Use a calculator. Round to the nearest hundredth. The solutions are about – 2.45 and about 2.45.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 1 Solve quadratic equations Solve the equation. 2. 5w 2 + 12 = – 8 SOLUTION 5w 2 + 12 = – 8 Write original equation.  w = –4 Take square roots of each side. Simplify. GUIDED PRACTICE ANSWER Negative real numbers do not have a real square root. So there is no solution. 5w 2 = – 8 –12 Subtract 12 from each side.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve quadratic equations Solve the equation. 3. 2x 2 + 11 = 11 SOLUTION 2x 2 + 11 = 11 Write original equation. x = 0 The root of 0 is 0. GUIDED PRACTICE ANSWER The solution is 0. 2x 2 = 0 Subtract 11 from each side.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 1 Solve quadratic equations Solve the equation. 4. 25x 2 = 16 SOLUTION 25x 2 = 16 Write original equation. Take square roots of each side. GUIDED PRACTICE Divided each to by 25. x = 16 25 x = ±  16 25 x = ± 4 5 Simplify. ANSWER The solution is – and. 4 5 4 5

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve quadratic equations Solve the equation. 5. 9m 2 = 100 SOLUTION 9m 2 = 100 Write original equation. Take square roots of each side. GUIDED PRACTICE Divided each to by 9. m = 100 9 m = ±  100 9 m = ± 10 3 Simplify. ANSWER The solution is – and. 10 3 3

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. EXAMPLE 1 Solve quadratic equations Solve the equation. 6. 49b 2 + 64 = 0 SOLUTION 49b 2 + 64 = 0 Write original equation. Take square roots of each side. GUIDED PRACTICE Divided each to by 9. 49b 2 = – 64 b2 =b2 = –64 49 Subtract 64 from each side. ANSWER Negative real numbers do have real square root. So there is no solution. b = – 64 49 

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve quadratic equations Solve the equation. Round the solution to the nearest hundredth. 7. x 2 + 4 = 14 SOLUTION x 2 + 4 = 14 Write original equation. Take square roots of each side. GUIDED PRACTICE Use a calculation. Round to the nearest hundredth. x 2 = 10 Subtract 4 from each side. ANSWER The solutions are about – 3.16 and 3.16. x =  10 + – x = + – 3.16

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve quadratic equations Solve the equation. Round the solution to the nearest hundredth. 8. 3k 2 – 1 = 0 SOLUTION 3k 2 – 1 = 0 Write original equation. Take square roots of each side. GUIDED PRACTICE Use a calculation. Round to the nearest hundredth. 3k 2 = 1 Add 1 to each side. k = + – 0.58 k2 =k2 = 1 3 k =  + – 1 3 Divided each to by 3. The solutions are about – 0.58 and 0.58.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solve the equation. Round the solution to the nearest hundredth. 9. 2p 2 – 7 = 2 SOLUTION 2p 2 – 7 = 2 Write original equation. Take square roots of each side. Use a calculation. Round to the nearest hundredth. 2p 2 = 2 + 7 Add 7 to each side. p = + – 2.12 p2 =p2 = 9 2 p =  + – 9 2 Divided each to by 2. GUIDED PRACTICE The solutions are about – 2.12 and 2.12.

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solving Quadratic Equations a.x 2 + 5 = 21 b.x 2 – 2 = 7 c.2x 2 = 18 d.3x 2 = 75

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solving Quadratic Equations a.2x 2 -8 = 0 b.x 2 +25 = 0 c.x 2 - 1.44 = 0 d.5x 2 = -15

9.1 – Students will be able to evaluate square roots.Students will be able to solve a quadratic equation by finding the square root. Solving Quadratic Equations a.3x 2 -48 = 0 b.120 - 6x 2 = -30 c.12x 2 - 60 = 0

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