1. Completing the Square and the Quadratic Formula
Objective: To solve quadratic equations by completing the square and using the quadratic formula.

3. Completing the Square
When completing the square, we follow the same technique each time.

4. Completing the Square
When completing the square, we follow the same technique each time.
Variables on one side, constants on the other.

5. Completing the Square
When completing the square, we follow the same technique each time.
Variables on one side, constants on the other.
Make sure the x2 is a 1x2.

6. Completing the Square
When completing the square, we follow the same technique each time.
Variables on one side, constants on the other.
Make sure the x2 is a 1x2.
Take half of the middle term and square it.

7. Completing the Square
When completing the square, we follow the same technique each time.
Variables on one side, constants on the other.
Make sure the x2 is a 1x2.
Take half of the middle term and square it.
Add that number to both sides.

8. Completing the Square
When completing the square, we follow the same technique each time.
Variables on one side, constants on the other.
Make sure the x2 is a 1x2.
Take half of the middle term and square it.
Add that number to both sides.
Solve

9. Completing the Square
Solve:

10. Completing the Square
Solve:
Add eight to both sides.

11. Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides.

12. Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides.
Solve.

13. Completing the Square Solve: Add eight to both sides.
Take half of 2, square it, and add it to both sides.
Solve.

14. You Try
Solve

15. You Try
Solve

16. You Try
Solve

17. Completing the Square
Solve:

18. Completing the Square
Solve:
Subtract 3 from both sides

19. Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2

20. Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2
Take half of 4, square it, add
to both sides

21. Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2
Take half of 4, square it, add
to both sides
Complete the square

22. Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2
Take half of 4, square it, add
to both sides
Complete the square
Take the square root and
solve.

23. Completing the Square Solve: Subtract 3 from both sides
Divide each side by 2
Take half of 4, square it, add
to both sides
Complete the square
Take the square root and
solve.

24. You Try
Solve

25. You Try
Solve

26. You Try
Solve

27. Vertex Form
After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

28. Vertex Form
After completing the square, the equation is in what we call vertex form since you can find the vertex from the equation.

29. Example 4

30. Example 4

31. The Quadratic Formula Given a quadratic equation of the form:
We can solve it using the quadratic formula:

32. The Quadratic Formula
Solve using the quadratic formula.

33. The Quadratic Formula Solve using the quadratic formula.
Set the equation equal to zero.

34. The Quadratic Formula Solve using the quadratic formula.
Set the equation equal to zero.
a=1, b=3, c=-9

35. The Quadratic Formula Solve using the quadratic formula.
Set the equation equal to zero.
a=1, b=3, c=-9
Use the quadratic equation.

36. The Quadratic Formula Solve using the quadratic formula.
Set the equation equal to zero.
a=1, b=3, c=-9
Use the quadratic equation.

37. The Quadratic Formula Solve using the quadratic formula.
Set the equation equal to zero.
a=1, b=3, c=-9
Use the quadratic equation.

38. You Try
Solve using the quadratic formula.

39. You Try Solve using the quadratic formula.
Set the equation equal to zero.
a=1, b=-3, c=-7
Use the quadratic equation.

40. Axis of Symmetry
The axis of symmetry for a parabola is the vertical line
This is also the x coordinate of the vertex. Put this back into the equation to find the y coordinate of the vertex.

41. Example 4

42. Example 4

43. You Try
Write the equation for the axis of symmetry and the vertex for the following.

44. You Try
Write the equation for the axis of symmetry and the vertex for the following.

45. You Try
Write the equation for the axis of symmetry and the vertex for the following.

48. Homework
Page 304
17-45 odd
Page 311
11-33 odd