1. Chapter 9 Modeling With Functions
Students will be able to transform quadratic and absolute value functions.
Students will be able to graph quadratic and absolute value inequalities.
Students will be able to solve system of equations involving quadratic equations.

2. Section 9.1
Students will learn how to shift, stretch, compress and reflect quadratic and absolute value functions.

3. Transforming the Quadratic Parent Function
F(x)=x^2
As a group determine how to do the following
Think of the vertex form of a quadratic function, or play around on your calculator
Move it left or right
Move it up or down
Make it narrow or wide (stretch vertically or horizontally)
Reflect it over the x axis
Reflect it over the y axis

4. Move it left or right
Add inside ( ) to move left
Subtract inside the ( ) to move right
Move it up or down
Add outside ( ) to move up
Subtract outside the ( ) to move down
Make it narrow or wide (stretch vertically or horizontally)
Number in front of the ( )
if >1 gets narrow or stretches vertically
if <1 gets wide or stretches horizontally
Reflect it over the x axis
Number in front of ( ) is negative
Reflect it over the y axis
x inside the ( ) is negative
Move first then reflect

5. Translations
These shifts can be written in the parent function Parent Function Up and Down Translation Left and Right Translation – notice the opposite of what is done inside the ( ) is what is done to the graph Vertex form of a parabola (h,k) is the vertex

6. From Equation
Can you state the translation if given the equation and sketch a graph

7. From Graph
Can you state translation from a graph and give the equation

8. Other Parent Functions
Do any of these ideas change for the other parent functions Absolute Value Cubic Square Root

9. Absolute value
How would the transformations be different/ the same for the absolute value function F(x)=|x| All the transformations are identical

10. Examples

11. Homework
Worksheet

12. Students will solve systems of equations and quadratic inequalities.
Section 9.2
Students will solve systems of equations and quadratic inequalities.

13. Gold Digger’s Gulch Pg 499 work through the problem
What equation did you get?
How many inequalities did you get and how?
When looking at the inequalities think of the warm-ups we did
How did we solve the inequality
How did we graph it

15. To Graph a Quadratic Inequality
Compare quadratic to zero
Factor the quadratic
Plot each zero on a number line
Test a point in each section of the number line (zeros break it into 3 parts) in the original equation
On the number line shade the regions that are true then write the inequality
Write the inequality

16. Number line and Terms
The zeros break the number line into 3 parts Lower boundary is to the left of the lowest number Upper boundary is to the right of the highest number Between the boundary is between the 2 zeros

17. Examples

18. Factoring If a =1 Factors of c that add to b (x factor 1)(x factor 2)
Divide everything by a negative then repeat above
If a is not 1
A times c
Factors that add to b
Rewrite equation using factors
Group 1st 2 terms, group 2nd 2 terms
Factor the groups
Group what is outside ( ) and multiply to what is inside the ( )

19. Systems of Quadratics
Use a calculator to do the following How else could you solve systems of equations Substitution, Elimination

20. Systems of equations Solving systems of equations with quadratics
Graphically – easiest using a calculator
Substitution
If linear and a quadratic solve linear for a variable and substitute into the quadratic
If both quadratic solve for y and set both equal to each other
Elimination – not used much
If linear and quadratic does it work
If both quadratic does it work

21. Example

22. Example

23. Homework
Worksheet on Inequalities and Systems You can check systems on calculator but must show either substitution or elimination