1 / 67

Solving Quadratic Equations

Solving Quadratic Equations. Review of Solving Quadratic Equations. ax 2 +bx +c = 0 A quadratic equation is a 2nd degree equation whose graph is a parabola. Solve with Perfect Square Binomial. Get Perfect Squares on Both Sides of Equation. Take Square Root of Perfect Squares

aspen-rowland
Download Presentation

Solving Quadratic Equations

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. Solving Quadratic Equations

  2. Review of Solving Quadratic Equations ax2 +bx +c = 0 A quadratic equation is a 2nd degree equation whose graph is a parabola.

  3. Solve with Perfect Square Binomial Get Perfect Squares on Both Sides of Equation. Take Square Root of Perfect Squares Solve Positive Number & Neg. Number Check Answers by Putting into Original Eq.

  4. Solve with Perfect Square Binomial Get Perfect Squares Binomial. Take Square Root of Both Sides of Eq Simplify Check Answers by Putting into Original Eq.

  5. Solve Quadratic Eq. By Factoring Set Eq = 0 Factor Set Each Factor = 0 Check Answers by Putting into Original Eq.

  6. What If You Can’t Factor The Equation? The “X” factor procedure doesn’t work which means it can not be factored -36 4

  7. You can solve this equation by Completing The Square CTS

  8. Review of a Trinomial Square (x+5)2 = x2 + 10x + 25 When you square a binomial you get a TRINOMIAL SQUARE

  9. What is Completing The Square? ? x2 + 10x + WHAT WILL MAKE A TRINOMIAL SQUARE?

  10. Now we will use these Algebra tiles to show Completing the Square 1 -1 x x2 -x -x2

  11. ? x2 + 10x + b It takes 25 ones to complete this square Note that 25 is half of b squared (10/2)2 = 52 = 25

  12. 2 b 2 Remember this to Complete The Square

  13. Finding Half of b Squared b

  14. Add to Complete the Square b This is now a trinomial square

  15. x2+6x+9 is a Trinomial Square x+3 x+3 x2+6x+9 (x+3)2 =x2 +6x+9

  16. More Examples of CTS Half of b Squared Half of b Squared

  17. More Examples of CTS Half of b Squared

  18. More Examples of CTS Half of b Squared

  19. Complete The Squareand State The Binomial Square

  20. Complete The Squareand State The Binomial Square

  21. Complete The Squareand State The Binomial Square

  22. Solve This Quad. Eq.

  23. If the “X” factor doesn’t work, you can’t solve by Factoring -31 4

  24. Solve by Completing The Square

  25. Solve by Completing The Square First Put c on One Side of equation.

  26. Solve by Completing The Square First Put c on One Side of equation. Divide by a Skip this step when a=1

  27. Solve by Completing The Square b First Put c on One Side of equation. Divide by a Complete The Square ADD HALF OF b SQUARED (b/2)2=(4/2)2=4

  28. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square Write Trinomial Square as a Binomial Square

  29. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square Write Trinomial Square as a Binomial Square Square Root both sides

  30. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square Write Trinomial Square as a Binomial Square Square Root both sides Solve for x (Note 2 Answers)

  31. Solve by Completing The Square First Put c on One Side of equation. Divide equation by a Complete The Square (b/2)2= 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  32. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2=(8/2)2=42=16 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  33. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2= 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  34. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2=(2/2)2=1 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  35. Solve by Completing The Square

  36. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2=(6/2)2=32=9 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  37. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2=(9/2)2= 81/4 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  38. Solve by Completing The Square First Put c on One Side of equation. Divide by a Complete The Square (b/2)2=(2/2)2=1 4. Write Trinomial Square as a Binomial Square 5. Square Root both sides 6. Solve for x (Note 2 Answers)

  39. Solve Quadratic Equations With The Quadratic Formula So far we have solved quadratic equations with FACTORING (Solves Equations with Integer Solutions) & COMPLETING THE SQUARE (Solves All quadratic equations) THE QUADRATIC FORMULA ALSO SOLVES ALL QUADRATIC EQUATIONS

  40. QUADRATIC EQUATION

  41. 2 + - b X= 2 a

  42. Solve with Quadratic Equation

  43. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0)

  44. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0) Plug a, b & c into the Quad. Eq.

  45. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0) Plug a, b & c into the Quad. Eq. Simplify Radical

  46. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0) Plug a, b & c into the Quad. Eq. Simplify Radical Solve for x

  47. Solve with Quadratic Equation

  48. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0)

  49. Solve with Quadratic Equation a=1 b c Put Equation into Std. Form (ax2+bx+c=0) Plug a, b & c into the Quad. Eq.

More Related