1. “Parabola and Your Life” Quadratic Functions

2. The Zeros of Quadratic Functions The zeros of Quadratic Function f(x) = ax 2 + bx + c can be found by letting f(x) = 0. Thus, 0 = ax 2 + bx + c

3. Connecting to Real Life A bookstore uses the quadratic function y = f(x) = - 0.00025x 2 + 0.105x – 1.025 as the formula that approximates the profit y for the number of books sold x. At what point does the bookstore start to lose money?

4. solution Set f(x) = 0 F(x)= -0.00025x 2 + 0.105x – 1.025 = 0 = -25x 2 + 10500x – 102 500 = 0 = -x 2 + 420x – 4 100 = 0 = x 2 – 420x + 4100 = 0 = (x-10)(x-410) = 0 X - 10 = 0 or x – 410 = 0 X = 10 x = 410 The company loses money if they sell fewer tha 10 books or more than 410 books.

5. http://www.youtube.com/watc h?v=1Pva-Iv43Nc

6. Methods Used to Solve Quadratic Equations 1. Factoring 2. Completing the Square 3. Quadratic Formula

7. Why so many methods? - Some methods will not work for all equations. - Variety is the spice of life. - Some equations are much easier to solve using a particular method.

8. Factoring Factoring is typically one of the easiest and quickest ways to solve quadratic equations; however, not all quadratic polynomials can be factored. This means that factoring will not work to solve many quadratic equations.

9. Factoring (Examples) 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. Completing the Square This method will work to solve ALL quadratic equations; however, it is “messy” to solve quadratic equations by completing the square if a ≠ 1 and/or b is an odd number. Completing the square is a great choice for solving quadratic equations if a = 1 and b is an even number.

11. Completing the Square (Examples Example 1 a = 1, b is even x 2 – 6x + 13 = 0 x 2 – 6x + 9 = –13 + 9 (x – 3) 2 = –4 x – 3 = ± 2i x = 3 ± 2i Example 2 a ≠ 1, b is not even 3x 2 – 5x + 2 = 0 OR x = 1 OR x = ⅔

12. Quadratic Formula This method will work to solve ALL quadratic equations; however, for many equations it takes longer than some of the methods discussed earlier. The quadratic formula is a good choice if the quadratic polynomial cannot be factored, the equation cannot be written as (x+c) 2 = n, or a is not 1 and/or b is an odd number.

13. Quadratic Formula (Example) x 2 – 8x – 17 = 0 a = 1 b = –8 c = –17

14. Real-life Bounce of a ball McDonalds sign Golf

15. “UPS” AND “DOWNS” UPS complete family 3 times a day to eat Studying When I passed the subject when I represented the school from quiz bee DOWNS Death of my mom, niece, and puppy. These UPS and DOWNS help me to become mature, stronger and a better person.

16. Resources: http://www.youtube.com/watch?v=1Pva-Iv43Nc Advanced algebra with trigonometry and statistics by Buzon, Olivia N. http://plus.maths.org/content/101-uses- quadratic-equation-part-i

17. Critique: It was informative and gives what is needed directly, however you should have made it more interesting (Ex. You can connect Parabola to your daily activities in life so that the student can be MORE motivated, or you can address practical issues that are solved using quadratic functions). -Askali Queenie