1. 2/15

2. (2v-3)(v+4) Do Now 2/15 Multiply:
Essential Question: What does the graph of a quadratic equation tell me?

3. Agenda Do Now Good things!!! Review: Factoring Notes:
Graphing Quadratic Equations
Interpreting information from graphs
Exit Ticket

4. Good Things!!! Independent practice due FRIDAY NO TUTORIALS TODAY
Tutorials tomorrow 2:45-3:45

5. Quick Review… a*c b Factoring! Factor Factor
What can I MULTIPLY to get my top number?
What can I ADD TOGETHER to get my bottom number?
a*c b
Factor
Factor

6. Quick Review… 1. Factor and solve for y: y2 – 7y + 12
2. Factor and solve for x:
3x2 – x – 10 

7. Notes “Building Graphs of Quadratic Functions” Worksheet
Number 1: f(x) = x2
Fill in the table with your partner
-Domain = x-values; Range = y-values
X-intercept: where y = 0; Y-intercept: where x = 0
Does this have a minimum or a maximum point?
Why are our y-values all greater than 0?
Why is the graph symmetric?

8. Notes Number 2: f(x) = x2 – 2x - 3 Fill in the table with your partner
-Domain = x-values; Range = y-values
X-intercept: where y = 0; Y-intercept: where x = 0
Does this have a minimum or a maximum point?
How does the y-intercept relate to the function?? Do we see it in our function?
Factor the function: how do the x-intercepts relate to the factors of the function?

9. Why might you need to know this?
Can you think of some jobs where you might need to be able to identify features of quadratic graphs? Why might you need to know intercepts and vertices?

10. Quadratic Graphs x2 – 2x – 3 Shape = Parabola
x-coordinate of vertex = -b/2a
x-coordinate of the vertex of a quadratic: -b/2a
Plug in to get y coordinate
See if this is true for the worksheet we just did (#2)
x2 – 2x – 3
b = -2, a = 1
-b/2a = -(-2) / 2(1) = 2/2 = 1
The x-coordinate of our vertex was at 1!

11. Quadratic Graphs What is a y-intercept?
The y-intercept occurs when x = 0.
When the quadratic equation is written in standard form, the y-intercept is c

12. Identify the y-intercept
f(x)= x2 + 6x + 9
Where is our vertex??
-b/2a
The axis of symmetry goes through the vertex

13. Quadratic Graphs Extremum The “extreme value” is Minimum when a > 0
Maximum when a < 0
Why??? Think about if the parabola is opening up vs opening down
Is the vertex at the top or the bottom?

14. Does the graph open up or down? Minimum or maximum?
f(x) = x2 + 6x + 9
f(x) = –3x2  + 24x – 48
m(b) = b2  – 6b + 10
f(x) = –7x2  – 14x – 6
What is the y-intercept of each function???
What is the vertex of each function??? Does it represent a minimum or maximum point?

15. Key Features of Quadratic Graphs
Given the function f(x) = –2x2 + 16x – 30, identify the key features of the graph: the extremum, vertex, and y-intercept.
Extremum: Does it open up or down?
Because a = –2, the graph opens down and the quadratic has a maximum
Vertex: x-coordinate = -b/2a
The x-coordinate of the vertex is 4
f(4) = 2. The y-coordinate of the vertex is 2. The vertex is at (4, 2)
Y-intercept: The y-intercept occurs when x = 0.
The y-intercept is (0, –30)

16. Key Features of Quadratic Graphs
Given the function f(x) = –2x2 - 12x – 10, identify the key features of the graph: the extremum, vertex, and y-intercept.
Extremum: Does it open up or down?
Because a = –2, the graph opens down and the quadratic has a maximum
Vertex: x-coordinate = -b/2a
The x-coordinate of the vertex is -3
f(-3) = 8. The y-coordinate of the vertex is 2. The vertex is at (-3, 8)
Y-intercept: The y-intercept occurs when x = 0.
The y-intercept is (0, –10)

17. Key Features of Quadratic Graphs
You KNOW the graph opens down, and you KNOW that the vertex is at (-3, 8).
Does this graph have ANY x-intercepts??? (without factoring!)

18. Does the graph have an x-intercept?
If the value of a is negative and the vertex is at (-10, -6), then how many x-intercepts will the graph have?
If the value of a is positive and the vertex is at (2, -4), then how many x-intercepts will the graph have?
If the value of a is positive and the vertex is at (7, 3), then how many x-intercepts will the graph have?

19. Practice problems

20. Your Turn! f(x) = x 2 + 6x + 9 1. Extremum 2. Vertex 3. Y-intercepts
4. Graph & make a table

21. Exit Ticket
What is the vertex of k(h) = h 2  – 4h + 3. Is this a maximum or a minimum?
What is the y-intercept of: f(x) = –7x2  – 14x – 6