1. 10.6 Using the Quadratic Formula

2. 10.6 – Quadratic Formula Goals / “I can…”  Use the quadratic formula when solving quadratic equations  Choose an appropriate method for solving a quadratic equation

3. 10.6 – Quadratic Formula We have used a couple of ways to find the zeros of a quadratic. 1.Graphing 2.Factoring 3.Square roots 4.Completing the square

4. y = x 2 – 4x – 5 Solutions are -1 and 5 10.6 – Quadratic Formula How many solutions are there? What are they?

5. 1. 25x 2 = 16 ANSWER 4 5 4 5 –, 2. 9m 2 = 100 ANSWER 10 3 –, 3 3. 49b 2 + 64 = 0 ANSWER no solution 10.6 – Quadratic Formula Use the Square Root method to solve:

6. Example 1 x 2 – 2x – 24 = 0 (x + 4)(x – 6) = 0 x + 4 = 0 x – 6 = 0 x = –4 x = 6 Example 2 x 2 – 8x + 11 = 0 x 2 – 8x + 11 is prime; therefore, another method must be used to solve this equation. 10.6 – Quadratic Formula

7. Solve x 2 – 16x = –15 by completing the square. SOLUTION Write original equation. x 2 – 16x = –15 Add, or (– 8) 2, to each side. – 16 2 2 x 2 – 16x + (– 8) 2 = –15 + (– 8) 2 Write left side as the square of a binomial. (x – 8) 2 = –15 + (– 8) 2 Simplify the right side. (x – 8) 2 = 49 10.6 – Quadratic Formula

8. However, each one is difficult if the zeros are decimals or fractions. Quadratic Formula The last way to find the zeros is to use the Quadratic Formula.

9. 10.6 – Quadratic Formula Quadratic formula Quadratic formula KNOW IT!!! LOVE IT!!! MEMORIZE IT (place it in your brain so that it can be recalled at anytime)

10. 10.6 – Quadratic Formula The letters a, b, and c refer to the letters in the quadratic equation: ax + bx + c = 0. 2

11. 10.6 – Quadratic Formula EXAMPLE: 7x – 2x – 8 = 0 Write down the letters: a = 7, b = -2, c = -8 2

12. 10.6 – Quadratic Formula Substitute the letters into the equation. = =1.22, - 0.94

13. 10.6 – Quadratic Formula

14. x 2 – 8x – 17 = 0 a = 1 b = –8 c = –17

15. a =b =c =110-7 10.6 – Quadratic Formula

16. How do you know which way to solve a quadratic equation? Graphing – calculator handy (easy x – int) y = x + 3 2

17. 10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Square roots – No bx term to solve x – 25 = 0 2

18. 10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Factoring – If it is easily factored x + x – 42 = 0 2

19. 10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Completing the square – Use if the x term is 1, but you CANNOT factor easily. x + 8x = 48 2 2

20. 10.6 – Quadratic Formula How do you know which way to solve a quadratic equation? Quadratic Formula – Use if the equation can’t be factored / easily factored. 7x – 2x – 8 = 0 2