1. AIM #1.5: How do we solve quadratic equations?

2. What is a quadratic Equation?

3. How do we solve quadratic Equations?
Square root Property
Factoring
Complete the square
Quadratic formula
Graphing (will visit in 1.5 B)

4. How do we solve quadratics using the square root property?

5. Example 1: Solve the quadratics

6. Check for Understanding:
Solve.
3𝑥 2 =27
𝑥+2 2 =25

7. What is the zero product principle?

8. How do we solve quadratics by factoring?

9. Example 2:
Solve by factoring.

10. Check for Understanding:
𝑥 2 −3𝑥 −10=0
𝑥 2 =8𝑥−15
3 𝑥 2 −2𝑥=8

11. How do we solve by completing the square?

12. Why do we call it complete the square?
Why we call this completing the square.

13. Example 3:
What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial.

14. Check for Understanding:
What term should be added to each binomial so that it becomes a perfect square trinomial? Write and factor the trinomial.
𝒙 𝟐 +𝟏𝟐𝒙
𝒙 𝟐 −𝟏𝟎𝒙

15. Solve using complete the square
Example 4:
Solve using complete the square

16. Check for Understanding:
Solve the equation by completing the square.
𝑥 2 +6𝑥=7

17. How do we solve using the quadratic formula?

18. Solve using the quadratic formula
Example 5:
Solve using the quadratic formula

19. Check For Understanding:
Solve using the quadratic formula.
3𝑥 2 −3𝑥−4=0

20. What is the function of the discriminant?

21. Example 6:
Compute the discriminant and determine the number and type of solutions:

22. Check for Understanding:
Compute the discriminant and determine the number and type of solutions:
𝑥 2 −4𝑥−5=0
2 𝑥 2 −11𝑥+3=0

23. Summary: Answer in complete sentences.
What are the four ways to solve quadratic equations?
For each equation below which strategy would recommend then solve.
𝟑 𝒙 𝟐 =𝟔𝟎
𝒙 𝟐 −𝟐𝒙=𝟏
𝒙 𝟐 −𝟔𝒙+𝟏𝟑=𝟎

24. Solution to summary: