1. Warm Up
Solve:
Answer

2. Lesson 15
Quadratic Functions

3. Basic Quadratic Function
Also known as Second Degree Function x y -4 -3 -2 -1 1 2 3 4 16 9 4 1 1 4 9 16

4. Quadratic Function - General form
Parameters a, b & c change the graph of a function.
Parameter “a”
- graph on graphing calculator

5. Quadratic Function - General form
Parameter “a”
- graph on graphing calculator

6. Quadratic Function - General form
Parameter "a" affects the opening of the parabola
a > 1: narrows the opening
a < 1: widens the opening
+ a (a > 0): the parabola is open upward
- a (a < 0): the parabola is open downward

7. Quadratic Function - General form
Parameter “b” - graph on graphing calculator
Parameter "b" creates an oblique translation of the parabola (ie diagonal shift)

8. Quadratic Function - General form
Parameter “c” - graph on graphing calculator
Graph
Parameter “c" is the initial value of the function (ie y-intercept)

9. Quadratic Function – Standard form
Parameters a, h & k change the graph of a function.
Parameter “a”
- graph on graphing calculator
Graph
Parameter "a" affects the opening of the parabola

10. Quadratic Function – Standard form
Parameter “h”
- graph on graphing calculator
Graph
Parameter “h" shifts the graph horizontally
(ie left and right)

11. Quadratic Function – Standard form
Parameter “k”
- graph on graphing calculator
Graph
Parameter “k" shifts the graph vertically
(ie up and down)

12. Quadratic Function – Standard form
If + a (a > 0), the parabola is open upward
If - a (a < 0), the parabola is open downward
The vertex of the parabola is: V (h, k)
The parabola's axis of symmetry is the vertical line passing through the parabola's vertex.
Its equation is : x = h
Graph

13. Quadratic Function – Standard form
Ex. Find the zero(s) of the following function:
Algebraically
- Zero(s)

14. Quadratic Function – Standard form
Ex. Find the initial value of the following function:
Algebraically
- Init Val.

15. Quadratic Function – Standard form
Finding the zero(s) of the Quadratic functions:
Find the zero(s) of the following function:

16. Quadratic Function – Standard form
Finding the zero(s) of the Quadratic functions:
Case 1: There are two zeros
Case 2: There is one zero
Case 3: There are no zeros

17. Homework
Workbook
P. 89 #1, Activity 3, 4, 5 & 6
P. 94 #3 & 4