Graphing Rational Functions Prerequisite Skills

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

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: 6x3 + 12x + 7x5 - x4

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

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?

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

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

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

Factoring Method #1 Greatest Common Factor

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

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

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

FACTOR:

FACTOR:

FACTOR:

Factoring Method #3 Factoring Trinomials when a=1

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

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

Ex: 3 Factor x2 - 16x + 64

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.

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

Factor

Factor

Solve by Factoring

1: Solve the equation x2 + x – 6 = 0

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

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?

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