1 / 22

CRASH COURSE IN QUADRATICS

Complete The Square. √. -b + b 2 – 4ac 2ac. (x+4)(x-3)=0. F O I L. (x+1)(x+2). X 2 – 5x +4. CRASH COURSE IN QUADRATICS. In preparation for the Algebra CST. Multiplying Polynomials. Area Model of Multiplication. 60 + 8. 30 + 4. To multiply 68 x 34:

hayden-cooper
Download Presentation

CRASH COURSE IN QUADRATICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Complete The Square √ -b + b2 – 4ac 2ac (x+4)(x-3)=0 F O I L (x+1)(x+2) X2 – 5x +4 CRASH COURSE IN QUADRATICS In preparation for the Algebra CST

  2. Multiplying Polynomials Area Model of Multiplication 60 + 8 30 + 4 • To multiply 68 x 34: • Write the two numbers in expanded notation and multiply one box at a time. • After you have multiplied the numbers, add all of the products together. 1800+240+240+32=2312 Now you try one… 48 x 53

  3. Multiplying Polynomials Area Model of Multiplication x + 2 x + 3 • To multiply (x+2)(x+3): • Write the two numbers in expanded notation and multiply one box at a time. • After you have multiplied the numbers, add all of the products together. X2 + + 6 5x Now you try one… (x+5)(x+1)

  4. Multiplying Polynomials FOIL ( x + 2 ) ( x + 3) = x2 + 5x + 6 (x)(x) = x2 First (x)(3) = 3x Outer (2)(x) = 2x Inner Last (2)(3) = 6 Combine like terms…

  5. Multiplying Polynomials x2 + 5x + 6 ax2 + bx + c a = 1 b = 5 c = 6

  6. Factoring Polynomials 10 6 14 12 2 5 6 1 7 2 3 4 7 7 9 7 21 18 6 3 5 4 9 10 Ask yourself… “What two numbers multiplied together give you the top digit and added together give you the bottom?”

  7. Factoring Polynomials X2 + 7x + 12 (x + )(x+ ) (x + )(x+ ) (x + )(x+ ) X2 + 13x + 36 -40 12 36 13 -6 7 X2 - 6x - 40

  8. Perfect Square Trinomial X2 + 12 + 36 (x + 6)(x + 6) (x + 6)2 X * X 6 * 6 X2 - 14 + 49 - (x - 7)(x - 7) (x - 7)2 X * X 7 * 7

  9. Solving Quadratic Equations • Graphing • Factoring • Using Square Roots • Completing the Square • Quadratic Formula

  10. Graphing Quadratic Equations x2 – 4x = 0 0 02 – 4(0) 0 0, 0 2 -4 2, -4 22 - 4(2) 4 42 – 4(4) 0 4, 0 The Solution is the ________________

  11. Find the solution for each graph:

  12. Factoring Quadratic Equations Using the Zero Product Property (x-3)(x+7)=0 (x-3)=0 (x+7)=0 x = 3 x = -7

  13. Factoring Quadratic Equations Solve using the Zero Product Property (x-3)(x+4)=0 (x+3)(2x-8)=0 (3x-1)(4x+1)=0 (3x+1)(8x-2)=0 Can you solve in your head? (x-2)(x+1)=0 -72 x2 - 21x = 72 x = x2 + 12x + 36 x = -21 • If x2 is added to x, the sum is 42. What are the values of x?

  14. Using Square Roots Square-Root Property x2 = 16 4x2 – 25 = 0 4x2 = 25 +25 +25 √4x2 = √25 √x2 = √16 2x = 5 x = +4 2 2 x2 = 16 x = + 2.5 (4)2= 16 (-4)2 = 16

  15. = 9 ( ) ( ) 6 2 6 2 2 2 ( ) b 2 2 Completing the Square Using Algebra Tiles x2 + 6x a= 1 b=6 c=0 x2 + 6x = 0 b = 6 + 9 + 9 x2 + 6x + 9 = 9 (x+3)(x+3)=9 (x+3)2 = 9 √(x+3)2 = √ 9 x+3= 3 x = 0 + x+3= 3 x+3= -3 x = -6

  16. Completing the Square Add to both sides of the equation ( ) 2 14 2 x2 + 14x = 15 b = 14 + 49 + 49 = 72 =49 Factor the Perfect Square x2 + 14x + 49 = 64 (x+7)(x+7)=64 (x+7)2 = 64 √(x+7)2 = √ 64 x+7= 8 x = 1 + x+7= 8 x+7= -8 x = -15

  17. Completing the Square Reduce 3x2 – 10x = -3 3 3 3 = 100 36 x2 - 10x = -1 3 b = 10 3 ( ) 2 Add to both sides of the equation -10 1 3 2 * x2 - 10x = -1 3 25 9 +25 9 +25 9 Factor the Perfect Square x2 - 10x + 25 = 16 3 9 9 -9 + 25 9 9 16 9 = 2 x – 5 = 4 3 3 x = 9 3 √ √( ) ( ) ( ) 2 x – 5 3 x – 5 3 x – 5 3 16 9 4 3 16 9 x = 1 3 = =+ = x – 5 = -4 3 3

  18. Completing the Square 2 x - 8x = 12 x - 8x = 5 What should be added to both sides of this equation? x + 4x = 6 x - 4x = 8 ax – bx = c 2 2 2 2

  19. The Quadratic Formula a = 1 b = 5 c = 6 x2 + 5x + 6 ax2 + bx + c a = 2 b = 3 c = -5 2x2 + 3x – 5 = 0 ax2 + bx + c -b +√ b2 – 4ac 2a x = -b +√ b2 – 4ac 2a -3 +√ 49 4 -3 +√ 9 – (-40) 4 -3 +√ 32 – 4(2)(-5) 2(2) -3 +7 4 x = x = x = x = x = -3 + 7 4 -3 - 7 4 x = x = x = 4 x = - 2.5

  20. The Quadratic Formula 2x = x2 - 3 ax2 + bx + c 2x = x2 - 3 0 = x2 – 2x - 3 -2x -2x a = 1 b = -2 c = -3 0 = x2 – 2x - 3 ax2 + bx + c 2 +√ 16 2 2 - 4 2 2 +√ 16 2 -b +√ b2 – 4ac 2a 2 +4 2 2 + 4 2 -(-2) +√ (-2)2 – 4(1)(-3) 2(1) -b +√ b2 – 4ac 2a 2 +√ 4 +12 2 -(-2) +√ (-2)2 – 4(1)(-3) 2(1) x = x = x = x = x = x = x = x = x = x = x = 3 x = -1

  21. Solving Quadratic Equations • Graphing • Factoring • Using Square Roots • Completing the Square • Quadratic Formula

  22. Solving Quadratic Equations 2 x + 4x - 2 = 0 x - 5x + 4 = 0 2

More Related