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Examples of Incredible Algebra Techniques

Examples of Incredible Algebra Techniques. DOTS: Difference of Two Squares. Traditional: a 2 – b 2 = (a – b)(a + b). 9x 2 – 16 . 3x 4 SS  Square Root, Square Root. 3x – 4 OM  One Minus. 3x + 4 OP  One Plus. 9x 2 – 16 = (3x – 4)(3x + 4) SS-OM-OP.

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Examples of Incredible Algebra Techniques

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  1. Examples of Incredible Algebra Techniques

  2. DOTS: Difference of Two Squares. Traditional: a2 – b2 = (a – b)(a + b) 9x2 – 16 3x 4 SS  Square Root, Square Root 3x – 4 OM  One Minus 3x + 4 OP  One Plus 9x2 – 16 = (3x – 4)(3x + 4) SS-OM-OP

  3. DOTS: Difference of Two Squares. 25x2 – 36 = (5x – 6)(5x + 6) 16x2 – 49 = (4x – 7)(4x + 7) 64x2 – 81= (8x – 9)(8x + 9)

  4. Square Trinomial Traditional: a2 + 2ab + b2 = (a + b)2 4x2 + 28x + 49 2x 7 SS  Square Root, Square Root (2x)(7)(2) = 28x MAD  Multiply And Double 2x 7 SS  Square Root, Square Root ( 2x + 7 )2 SSMAD (use the middle sign)

  5. Square Trinomial Traditional: a2 – 2ab + b2 = (a – b)2 9x2 – 30x + 25 3x 5 SS  Square Root, Square Root (3x)(5)(2) = 30x MAD  Multiply And Double 3x 5 SS  Square Root, Square Root ( 3x – 5 )2 SSMAD (use the middle sign)

  6. Square Trinomial 16x2 – 72x + 81 4x 9 SS  Square Root, Square Root (4x)(9)(2) = 72x MAD  Multiply And Double 4x 9 SS  Square Root, Square Root ( 4x – 9 )2 SSMAD (use the middle sign)

  7. Factoring a Trinomial • = 36 3x2 – 20x + 12 – 20 1x36 – 2x – 18x – 2 – 18 2x18 3x2 – 2x – 18x + 12 3x12 x(3x– 2) x(3x– 2) (3x – 2) x(3x– 2) – 6(3x – 2) 4x9 (3x– 2)( x – 6) 6x6

  8. Singing the Quadratic Formula X equals negative b, plus or minus the square root, Of b squared minus 4 ac All over 2 a.

  9. Polynomial Graph – End Behavior f(x) = 5x3 f(x) = – 5x3 Leading coefficient is positive so RISES RIGHT. Leading coefficient is negative so RISES LEFT

  10. Polynomial Graph – End Behavior f(x) = 5x3 Leading coefficient is positive so RISES RIGHT. DiscoRight

  11. Polynomial Graph – End Behavior f(x) = – 5x3 Leading coefficient is negative so RISES LEFT Disco Left

  12. Find the slope of the line joining the points (2, 4) and (5, 3). Traditional method Forwards method

  13. 2) Find the slope of the line joining the points (-5,7) and (-3, -8). 1) Find the slope of the line joining the points (3,8) and (-1,2).

  14. This method is used to find a second point on the line if you know a point and the slope. Find the next point on the line using the slope. y If m = 2 =y rise = 2 = y run = 5 = x From (4, 8) find the next point. 2 5 5 x r I S e run Christine’s Method (x , y) + = 5 (9, 10) (x, y) 2 (4, 8) (x , y) (4, 8) (9 , 10) x

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