1. Graphing Rational Functions
Prerequisite Skills

2. The Anatomy of a Polynomial
6a3 – 5a2 + 3a - 9
coefficients
constant
leading coefficient
*Standard Form: Arranging your terms from highest exponent to lowest exponent.

3. The _________exponent in the polynomial determines the DEGREE OF A POLYNOMIAL.
EX: The degree of – 4x2 + 4x - 9 is ____ because ___ is the highest exponent in the polynomial.
EX: Find the degree of the following polynomial: 6x x + 7x5 - x4

4. Polynomial
Standard Form
Degree
Leading Coefficient 7x
19 – 8x
4x3 - 3
-5x4 + 2x2
1 + x2 – 7x
2x5 –x3 + 8x2 –3

5. Finding the Y-Intercepts of a Function
The y-intercepts are the points where the graph touches or crosses the _________________.
What is the y-intercept of the following graphs?

6. The y-intercepts are those points where x = ______
The y-intercepts are those points where x = ______ . Therefore, to find the y-intercepts of a function, plug in a zero for x and solve for y.
Examples: Find the y-intercept of each function.
1) y =2x + 1
2) y = 5 – 3x
3) -2x – 9y = 7

7. The y-intercepts are those points where x = ______ . Therefore, to find the y-intercepts of a function, plug in a zero for x and solve for y.
Examples: Find the y-intercepts of each function.
4) x + 4y = 4
5) y = -8x2 – 9
6) y = -4x2 – 4x + 8

8. Factoring Polynomials
Greatest Common Factor
Difference of Squares
Trinomials, where a = 1
Trinomials, where a ≠ 1

9. Factoring Method #1
Greatest Common Factor

10. Factor
6x2 – 8x
What is their GCF?
2a3 – 6a
What is their GCF?

11. Factor
2h2k + 2k
What is their GCF?
6uv + 9v2
What is their GCF?

12. Factoring polynomials that are a Difference of Squares.
Factoring Method #2
Factoring polynomials that are a Difference of Squares.

13. FACTOR:

14. FACTOR:

15. FACTOR:

16. Factoring Method #3
Factoring Trinomials when a=1

17. To FACTOR a trinomial means to write it as the product of two binomials.
Factor x2 + 6x + 8 8
What two numbers ultiply to give you the last number…
and add to give you the middle number? 6

18. Ex: 2
Factor x2 - 3x + 2
What two numbers multiply to give you the last number…
and add to give you the middle number?

19. Ex: 3
Factor x2 - 16x + 64

20. Always check for GCF before you do anything else.
Factor Completely:
Don’t Forget Method #1.
Always check for GCF before you do anything else.

21. Factoring Method #4 Factoring Trinomials when a ≠ 1
Use the Kickback Method!

23. Factor

24. Factor

25. Solve by Factoring

26. 1: Solve the equation x2 + x – 6 = 0

27. 2: Solve the equation x2 + 10x + 25 = 0

28. Finding the X-Intercepts of a Function
The x-intercepts are the points where the graph touches or crosses the ______________ .
What are the x-intercepts of the following graphs?

29. Examples: Find the x-intercepts of each function.
The x-intercepts are those points where y = ______ . Therefore, to find the x-intercepts of a function, plug in a zero for y, factor, and solve for x.
Examples: Find the x-intercepts of each function.
1) y = x2 – 2x - 15
2) y = x2 –x - 6
3) y = x2 – 2x - 63
4) y = x2 –5x + 6