Examples of Incredible Algebra Techniques.

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Presentation transcript:

Examples of Incredible Algebra Techniques

DOTS: Difference of Two Squares. Traditional: a2 – b2 = (a – b)(a + b) Incredible: a2 – b2 = SS-OM-OP 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

DOTS: Difference of Two Squares. Incredible: a2 – b2 = SS-OM-OP 25x2 – 36 = (5x – 6)(5x + 6) 16x2 – 49 = (4x – 7)(4x + 7) 64x2 – 81= (8x – 9)(8x + 9)

Square Trinomial Incredible: a2 + 2ab + b2 = SSMAD Traditional: a2 + 2ab + b2 = (a + b)2 Incredible: a2 + 2ab + b2 = SSMAD 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)

Square Trinomial Incredible: a2 – 2ab + b2 = SSMAD Traditional: a2 – 2ab + b2 = (a – b)2 Incredible: a2 – 2ab + b2 = SSMAD 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)

Square Trinomial Incredible: a2 – 2ab + b2 = SSMAD 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)

Factoring a Trinomial Incredible: Backwards foil = 36 - 20 36 + x 3x2 – 20x + 12 – 20 1x36 – 2x – 18x – 2 – 18 2x18 3x2 – 2x – 18x + 12 3x12 x(3x – 2) – 6(3x – 2) x(3x – 2) (3x – 2) x(3x – 2) 4x9 (3x – 2)( x – 6) 6x6

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

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

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

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

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

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

Find the next point on the line using the slope. 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) (4, 8) (x , y) (9 , 10) x