1. 2-2: Solving Quadratic Equations Algebraically
Learning Goals:
Solve by factoring
Solve by taking square root of both sides
Solve by completing the square
Solve by using quadratic formula
© 2007 Roy L. Gover (

2. Definition
A quadratic, or second degree equation is one that can be written in the form
for real constants a,b, and c with a≠0. This is the standard form for a quadratic equation.

3. Important Idea
There are 4 techniques to algebraically solve quadratic equations:
Factoring
Taking square root of both sides
Completing the square
Using quadratic formula

4. Example
Solve by factoring:

5. Definition
The zero product property: If the product of real numbers is zero, then one or both of the numbers must be zero

6. Example
What is wrong with this:
Solve by factoring:

7. Try This Solve by factoring:
Can you think of a way to check your answer?

8. Try This
Solve by factoring:
Hint: write in standard form

9. Example
Solve by taking the square root of both sides: a. b.

10. Try This
Solve by taking the square root of both sides:

11. Try This
Solve by taking the square root of both sides. Give exact and approximate solutions.

12. Example What is wrong with this?
Solve by taking the square root of both sides:

13. Example Complete the square for:
1. Half the coefficient of x: 1/2 of 12=6
2. Square this number and add to the expression

14. Important Idea
Completing the square is the process of finding the number that will make the expression a perfect square trinomial.

15. Important Idea
is a perfect square trinomial because it factors as:

16. Try This
Complete the square for:
then factor your result

17. Example Complete the square for: then factor your result.
Use fractions only.

18. Example Solve by completing the square:
1. Move the constant to the right:

19. Example Solve by completing the square:
2. Complete the square and add to the left and right:

20. Example
Solve by completing the square:
3. Factor left side and solve:

21. Try This
Solve by completing the square:

22. Example Solve by completing the square…
Before you complete the square, the coefficient of the squared term must be 1

23. Try This
Solve by completing the square…fractions only.

24. Definition The solutions to are:
These solutions are called the Quadratic Formula

25. Important Idea is called the discriminant 1. If
there are 2 real solutions

26. Important Idea is called the discriminant 2. If
there is 1 real solution

27. Important Idea is called the discriminant 3. If
there are no real solutions

28. Example
Solve using the quadratic formula. Leave answer in simplified radical form.

29. Try This
Solve using the quadratic formula. Leave answer in simplified radical form.

30. Example
Solve using the quadratic formula. Leave answer in simplified radical form.

31. Lesson Close
State the quadratic formula from memory.

32. Practice
1. 95/1-23 odd (slides 1-12)
2. 95/26-34 even (slides 13-32)