Download presentation

Presentation is loading. Please wait.

Published byTracy Craig Modified over 5 years ago

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. 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

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. 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

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.

4
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.

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. 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.

6
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

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.

8
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
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

10
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

11
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

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. 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

13
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

14
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

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. 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.

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. 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.

17
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.

18
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.

19
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

20
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.

21
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.

22
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.

23
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

24
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

25
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

26
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

27
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.

28
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.

29
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

30
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

31
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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google