1. “Parabola and Your Life”
Quadratic Functions

2. The Zeros of Quadratic Functions
The zeros of Quadratic Function f(x) = ax2 + bx + c can be found by letting f(x) = 0. Thus,
0 = ax2 + bx + c

3. Connecting to Real Life
A bookstore uses the quadratic function y = f(x) = x x – 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)= -0.00025x2 + 0.105x – 1.025 = 0
X - 10 = 0 or x – 410 = 0
X = x = 410
The company loses money if they sell fewer tha 10 books or more than 410 books.

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.
- Some equations are much easier to solve using a particular method.
Variety is the
spice of life.

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) x2 – 2x – 24 = 0 (x + 4)(x – 6) = 0
x2 – 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
a ≠ 1, b is not even
3x2 – 5x + 2 = 0
Example 1
a = 1, b is even
x2 – 6x + 13 = 0
x2 – 6x + 9 = –13 + 9
(x – 3)2 = –4
x – 3 = ± 2i
x = 3 ± 2i 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)
x2 – 8x – 17 = 0
a = 1
b = –8
c = –17

14. How importance is parabola to you?
One of the benefits of Quadratic Functions to us is when we play basketball.

15. What are your “UPS” and “DOWNS” in life and how these affect you?
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 help me not to give up but help me to become a better person

16. Resources: http://www.youtube.com/watch?v=1Pva-Iv43Nc
Advanced algebra with trigonometry and statistics by Buzon, Olivia N.

17. ROLES Jomar Lapayag – Secretary, Researcher
Jomar Vitor Lapayag – Researcher, Presentor
Jomarvelous Lapayag – Presentor, Analyst
Jomarvelous Vitor Lapayag – Analyst, Powerpoint Presentation maker