1. Homework Review
Lesson 3.1B

2. Characteristics of Quadratics
Unit 5c

3. Graphing a Quadratic Function
EQ: How do we identify all of the important characteristics of a quadratic?
Lesson 3.1B

4. Today, we are going to begin by reviewing what we have learned yesterday from graphing in vertex form.
Lets recall how to find the following:
Vertex
Axis of Symmetry
Maximum or Minimum
Y-intercept

5. c) Since a > 0 , the parabola opens up and has a: minimum
Find: a) vertex
b)axis of symmetry
c) state whether the vertex is a maximum or minimum.
d) y-intercept
Shifted up 2 units
a) Vertex:
(0, 2)
b) Axis of symmetry:
x = 0
c) Since a > 0 , the parabola opens up and has a:
minimum
d) y-intercept:
(0, 2) 5

6. Reflected about x-axis Left 2 units Up 4 units
Find: a) vertex
b) axis of symmetry
c) state whether the graph has a maximum or minimum.
d) y - intercept
Reflected about x-axis
Left 2 units
Up 4 units
a) Vertex:
(-2, 4)
b) Axis of symmetry:
x = -2
c) Since a < 0 , the parabola opens down and has a:
maximum
d) y-intercept:
(0, 0) 6

7. Domain VS. Range Domain: (x – values) read domain from left to right
Range: (y-values) read range from bottom to top

8. The DOMAIN of parabolas is all real numbers…
unless the parabola looks like this and has endpoint(s)
We say the domain is restricted, therefore it is no longer all real numbers 8

9. Find the domain of the graph below
-1 < x < 2 9

10. Domain: -2 < x < 2 Range: 0 < x < 4
Find the domain and range of the graph below
Domain:
-2 < x < 2
Range:
0 < x < 4 10

11. Domain: -∞ < x < ∞ Range: -∞ < x < 4
Find the domain and range of the graph below
Domain:
-∞ < x < ∞
Range:
-∞ < x < 4 11

12. Graph the quadratic using the axis of symmetry and vertex.
Y-intercept:
Max or Min?
maximum
Extrema:
y = 3
Domain:
Range:
All real numbers
y ≤ 3 12

13. Graph the quadratic using the axis of symmetry and vertex.
(-1, 0)
Axis of symmetry:
Y-intercept:
Max or Min?
minimum
Extrema:
y = 0
Domain:
Range:
All real numbers
y ≥ 0 13

14. What are these lines doing from left to right?
Intervals of
increase and decrease
To determine the intervals of increase and decrease, you must “read” the graph from left to right
What are these lines doing from left to right? 14

15. Let’s apply this idea to parabolas…
To determine the intervals of increase and decrease, you must “read” the graph from LEFT to RIGHT
What is this parabola doing on the left side of the vertex?
What is this parabola doing on the right side of the vertex?
Going downhill
Going uphill
Interval of decrease
Interval of increase 15

16. One more… Going uphill Going downhill
What is this parabola doing on the left side of the vertex?
What is this parabola doing on the right side of the vertex?
Going uphill
Going downhill
Interval of decrease
Interval of increase 16

17. Graph each quadratic function and determine the interval of increase and decrease
y = (x+1)²+2
Interval of decrease
Interval of increase 17

18. Graph each quadratic function and determine the interval of increase and decrease
Interval of decrease
Interval of increase 18

19. Determine if the given interval is an interval of increase or decrease19

20. Rate of Change
To determine the rate of change, find the slope of the line that passes through two given points on the function. 20

21. Find the rate of change on the interval: -1≤x≤221

22. End Behavior
The value a function, f(x), approaches when x is extremely large (∞) or when x is extremely small (-∞). 22

23. Even and Odd Functions

24. Assignment: Practice Worksheet24