1. Chapter 5
Quadratics: Make connections between different representations of the quadratic function. You will also solve the quadratic equation using multiple methods.

2. 5.1 Multiple Representations and Description of
Students will explore graphs, tables and equations of quadratics. Students will learn and apply the zero product rule to find x-intercepts. Students will solve real world problems.

3. 5.1.1 Graph of a Quadratic
When graphing a quadratic function you get a parabola Looks like the letter U Domain is all real numbers Range is limited by the turning Point or vertex

4. 5.1.1 Describing a Parabola Depends on what is given
graph, table or equation
But you should be able to describe the following
Which direction does the parabola open
Is it narrow (skinny) or wide (fat)
What is the vertex
What are the x-interepts
Axis of symmetry
What is the y-intercept

5. Based on Graph
Opens up (can hold water) or down (won’t hold water) Narrow or Wide – look at distance between sides Vertex – turning point in graph, this should be an ordered pair Axis of symmetry – vertical line through the vertex X-intercepts – order pairs where graph crosses the x-axis, could be 0,1 or 2 Y-intercept – ordered pair where it crosses the y axis only 1

6. Example
Describe the following parabola

7. Equation
Vertex form Factored form Standard form Each form has is pros and cons we will look at throughout this unit

8. From equation
Opens up if a value is positive Opens down if a value is negative Narrow if |a|>1 Wide if |a|<1 We will talk about how to calculate x-intercepts later using multiple methods Vertex – depends on the form given, will talk more about this calculation later Y-intercept sub in zero for x and solve

9. Calculating Characteristics
Vertex The second part of the ordered pair means to sub in the first coordinate into the equation and solve for the second Axis of symmetry X-intercepts try factoring the polynomial

10. Example
Describe what the graph would look like given the equation, graph in calculator to see if you are correct

11. Homework
Worksheet

12. 5.1.2 Connections
As a group turn to page 264 read through and work on 5-16 Collect a resource page from the back table to do this Now work through 5-17

13. 5.1.3 Sketch
A sketch is being able to plot specific points and connect them
These specific points are
Vertex – we already discussed how to find
Y-intercept – we already discussed how to find
X-intercepts – we will use what is called the zero product property, which we have discussed just not named.

14. Zero Product Property
Finding the zeros of a quadratic is the same as finding the x-intercepts
What x values would make the equation equal to zero
Factor the trinomial completely
Set each of the factored parts equal to zero and solve
Each part could equal zero separately because when you multiply by zero you will always get zero
Ask yourself these questions and we do some problems
Did you notice any short cuts
Did you notice any thing to determine the number of zeros

15. Examples

16. Homework
Worksheet

17. 5.1.4 Writing the quadratic equation
How can you write an equation given a table of data? How can you write an equation given a graph of the data? As a group work on problem 5-39 on page 273 Try to come up with a process on how to write the equation that represents this table.

18. Solutions Find the x-intercepts Find the y-intercept
Use idea of zero product rule to write out factored form of the quadratic, with x-intercepts
Use y-intercept to help determine a value

19. Example Pg

20. Homework
Pg show all work needed to support your answer

21. 5.1.5 Connections
As a group work through 5-49 on page 277 Make sure you can explain your choices 5-51 pg 279

22. Homework Pg