![x2
- 7x + c
c = (b
/2)2
• What is b? -7
[remember ax2
+ bx + c?]](https://image.slidesharecdn.com/a25-5completingsquare-101109161626-phpapp01/85/A25-5-Completing-the-Square-15-320.jpg)
A25-5 Completing the Square
- 1. Graphing Complex Numbers Algebra 2 5.4 Part 3 p. 273
- 2. Graphing Complex Numbers • Real axis
- 3. Graphing Complex Numbers • Real axis • Complex or Imaginary axis
- 4. Graphing Complex Numbers • To graph the number a + bi
- 5. Graphing Complex Numbers • To graph the number a + bi • Go to a on the Real axis.
- 6. Graphing Complex Numbers • To graph the number a + bi • Go to a on the Real axis. • Go to b on the Imaginary axis.
- 7. Graphing Complex Numbers • For example: graph 2 - 3i. • Out 2
- 8. Graphing Complex Numbers • For example: graph 2 - 3i. • Out 2 • Down 3
- 9. Graphing Complex Numbers • For example: graph 2 - 3i. • Out 2 • Down 3 2 - 3i
- 10. Complex Numbers • The absolute value of a complex number is the distance from the origin.
- 11. Completing the Square Algebra 2 5.5 p. 282
- 12. Binomial Theorem a2 + 2ab + b2 = (a + b)2
- 13. Binomial Theorem a2 + 2ab + b2 = (a + b)2 I.e., x2 + 4x + 4 = (x + 2)2
- 14. x2 - 7x + c c = (b /2)2
- 15. x2 - 7x + c c = (b /2)2 • What is b? -7 [remember ax2 + bx + c?]
- 16. x2 - 7x + c c = (-7 /2)2
- 17. x2 - 7x + c c = (-7 /2)2 = 49 /4 • Square the top, square the bottom
- 18. x2 - 7x + 49 /4 Can we factor this?
- 19. x2 - 7x + 49 /4 = (x - 49 /4)2
- 20. Completing the Square • Move the constant term to the opposite side of the equal sign of the x-terms.
- 21. Completing the Square • Move the constant term to the opposite side of the equal sign of the x-terms. • Find c. • Add c to both sides of the equal sign.
- 22. Completing the Square • Move the constant term to the opposite side of the equal sign of the x-terms. • Find c. • Add c to both sides of the equal sign. • Factor the left side. • Take the square root of both sides.
- 23. Completing the Square • Move the constant term to the opposite side of the equal sign of the x-terms. • Find c. • Add c to both sides of the equal sign. • Factor the left side. • Take the square root of both sides. • Solve for x and simplify.