1. Warm Up
Identify the following and then sketch the graph:
Direction of opening
Y-intercept
Vertex
AOS
Zeros (factor)
Max or Min
f(x) = 2x2 – 10x + 12

2. Quadratic Properties: Increasing, Decreasing, & Interval Notation
Sept. 15th

3. Number of Solutions (zeros, roots)
If the parabola is completely above or below the x-axis, we say there are NO Real Solutions.
If the parabola sits on the x-axis, we say there is ONE Real Solution.
If the parabola is on both sides of the x-axis (crosses the axis twice), we say there is TWO Real Solutions.

4. Review (quadratics): What can we get …
From the Graph:
From the Equation:

5. Domain and Range
Domain: The set of x-values that exist on the function
What values of the x-axis are covered by the graph?
For Quadratics, this is ALWAYS: -∞ to ∞
Range: The set of y-values that exist on the function
- What values of the y-axis are covered by the graph?

6. What are the Domain & Range?

7. What are the Domain & Range?
Give the domain and range for these graphs …

8. Increasing vs. Decreasing
Properties to consider:
The direction of the opening of a parabola
Don’t forget about your end behavior!!

9. Intervals
We can show the region of the graph that is increasing and decreasing by an interval.
Intervals describe the range of x-values that meet the given requirement (where the graph is increasing or decreasing).

10. Increasing vs. Decreasing
In this graph, the interval where the parabola is increasing is from - (remember the end behavior) to -1.
The graph is decreasing
from _____ to _____.

11. Increasing vs. Decreasing
Discuss with a partner where the graph is increasing and decreasing. Describe in the way we just did where the graphs are increasing and where they are decreasing.

13. Interval Notation
We use interval notation to abbreviate the description.
List the starting and ending points of your interval, separated by a comma.
- to -1 will look like: -, -1
Then we decide if there should be parentheses ( ) or brackets [ ]

14. Interval Notation
**Parentheses indicate that the graph does not include the endpoint
**Brackets indicate that the graph does include the endpoint
On a graph, we can see this with open and closed circles
Open Circles indicate we are NOT including the point: ( )
Closed Circles indicate that we ARE including the point: [ ]

15. Let’s Try using Inequalities:
1. What does x ≤ -2 look like on a number line?
Using the number line, how could we write this in interval notation?
2. Now lets try x > 5

16. Partner Activity Graph the inequality and Write in Interval Notation:
x ≤ -5
x > 10
x < 2
Draw each interval on a number line:
1. (-∞, -8]
2. [5, ∞)
3. (1, 5)

17. Interval notation
Now, use interval notation to describe where the graphs are increasing and decreasing (the graph you discussed with your partner).

18. Try These Graphs

19. Now Let’s Use Interval Notation for Domain and Range

20. Now find the Domain and Range of these graphs

21. Translation
Sometimes we have graphs that increase/decrease in more than one place.
Rather than write out the word “and” we use the symbol “”
We call this a Union.

22. Let’s look again…
Using our new math vocabulary and our knowledge of interval notation, describe the increasing and decreasing parts of the graph. And the domain and range.

23. Homework
Quadratics Properties Worksheet

24. Poster Project You will be making 2 Posters Tomorrow!
You will work TOGETHER with 1 – 2 other people
This is NOT an individual task that multiple people put their name on
I will have up what is needed for the poster
I will come around and give you the materials you need (2 posters for each group)
This will be a QUIZ GRADE so use the time I am giving you and work you hardest!

25. Posters Project Equation Table x and y values Sketch of the Graph
Find and Label the y-intercepts
Find and Label the vertex
Give the Axis of Symmetry
Give the min/max Value
Give the Direction of Opening
Zeroes if they can be Identified
Interval Notation for Increasing and Decreasing Curves
Interval Notation for Domain and Range

26. Flex: Factoring Review
Factor the following expressions:
x2 – 15x + 50
12xy – 4y + 9x – 3
x2y - 3x2 – 8y + 24
x2 – 36
20x2 – 16x
4x2 - 24x + 36
2x3 + 12x2 + 16x
x2 - 5x- 14
15ab – 5b + 9a – 3