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# Quadratic Equation solved by Square root property

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Lesson 1 Grade 9 k to 12

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### Quadratic Equation solved by Square root property

1. 1. PRIMING ACTIVITY DEPARTMENT OF EDUCATION An ANAGRAM is a type of word play, the result of rearranging the letters of a word or phrase to produce a new word or phrase, using all the original letters exactly once. Example CARTHORSE can be rearranged into ORCHESTRA.
2. 2. DEPARTMENT OF EDUCATION Anagram of the word GRAB LEA 10987654321 ALGEBRA 0
3. 3. DEPARTMENT OF EDUCATION Anagram of the word ACID QUART 10987654321 QUADRATIC 0
4. 4. DEPARTMENT OF EDUCATION Anagram of the word PEN XEROSIS 10987654321 EXPRESSION 0
5. 5. DEPARTMENT OF EDUCATION Anagram of the word ON A QUIET EQUATION 109876543210
6. 6. DEPARTMENT OF EDUCATION Anagram of the word ACTING FOR FACTORING 109876543210
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24. 24. Lessons Lesson 1: Illustrations of Quadratic Equations Lesson 2: Solving Quadratic Equations  Extracting Square Roots  Factoring  Completing the square  Using the Quadratic Formula Lesson 3 : Nature of Roots of Quadratic Equations
25. 25. Lesson 4: Sums and Product of the Roots of Quadratic Equations Lesson 5: Equations Transformable to Quadratic Equations (Including Algebraic Equations) Lesson 6 : Applications of Quadratic Equations and Rational Algebraic Equations Lesson 7 : Quadratic Inequalities
26. 26. 1.Choose a leader 2.Secretary 3.2 Presenters 12 min11 min10 min9 min.8 min7 min6 min5 min4 min3 min2 min1 min1098765432210
27. 27. 1. How did you find the product? 2. In finding each product, what mathematics concepts or principles did you apply? Explain how you applied these mathematics concepts or principles? 3. How would you describe the products obtained? 4. Are the products polynomials? If YES, what common characteristics do these polynomials have?
28. 28. 1. How do you describe Linear equation? 2. How are these equations different from those which are linear? 3. What common characteristics do these equations have?
29. 29. Activity1: Find My Roots Directions: Find the following square roots. 1.) 16 2. ) – 25 3.) 49 4.) – 64 5.) 121 6.) – 289 7.) 0.16 8.) ± 36 9.) 16 25 10.) ± 169 256 = 4 = –5 = 7 = –8 = 11 = – 17 = 0.4 = ± 6 = 4 5 ± 13 = 16
30. 30. Extracting Square Roots Quadratic equations that can be written in the form x2 = k ca be solve by applying the following properties: 1.) If k > 0, then x2 = k has two real solutions or roots: x = ± k2.) If k = 0, then x2 = k has one real solutions or root: x = 03.) If k < 0, then x2 = k has no real solutions or roots: Examples: x2 – 16 = 0 x2 = 16 x = ± 16 x = ± 4 x2 + 10 = 10 x2 = 10 – 10 x2 = 0 x2 + 9 = 0 x2 = –9 no real roots
31. 31. Factoring How do you factor the following?: 1.) x2 + 8x – 9 x x Factors of – 9 9 ; -1 -9 ; 1 Sum of factors8 -8 + 9 – 1 OR x2 -9-x 9x x 9 x -1 ( x + 9 ) ( x – 1 ) -3 ; 3 0
32. 32. 2.) 3x2 – x – 10 – 30x2 - 30x2 = factors Sum of factors-30x ; x 30x ; -x -15x ; 2x 15x ; -2x -6x ; 5x 6x ; -5x -29x 29x -13x 13x -x x 3x2 – 6x + 5x – 10 (3x2 – 6x) + (5x – 10) 3x(x – 2) + 5(x – 2) O R 3x 2 -105x -6x x -2 3x 5