Unit 13 Day 2 Polynomials.notebook April 05, 2018Good afternoon! Please...

[1] Take out your packet

[2] Grab a chrome book & white board materials

[3] Complete warm upUsing finite differences, determine the degree of the following polynomials.

x y1. 2. x y

-10123

162

-2420

1

45

23

-6-14914

Any questions from the Homework?

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Unit 13 Day 2: Polynomials

I can find the x,y intercepts of a polynomial equation

I can convert from factored to general form

I can solve for the scale factor of a polynomial

Polynomial FunctionsQuadratic:  f (x) = 3x2 + 5x – 7

Cubic:    f (x) = 7x3 ­ 5x2 + 3x – 1

Quartic:  f (x) = 2x4 ­ 6x3 + 2x + 5

Quintic:  f (x) = 11x5 ­ 2x2 

Recall: 

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Polynomial FunctionsHow does the degree relate to the shape?

Identify the x­intercepts and degree, then write a possible equation. 

Unit 13 Day 2 Polynomials.notebook April 05, 2018

An nth degree polynomial function has exactly n zeros.

FUNDAMENTAL THEOREM OF ALGEBRA

(both real and complex)

What is the connection between the # of roots and the degree of the polynomial? 

Sketch a graph for the following scenarios:

1. A quadratic function with 2 real roots.

2. A quartic function with 2 real roots.

3. A cubic function with only 1 real root.

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Find x­intercepts and y­intercepts and graph on your calculator to check

y = ­0.5(x ­ 3)(x ­ 2)(x + 4) 

y = 3(x ­ 4)2 Convert to general form: 

x int _______ 

y int _______

x int _______ 

y int _______

Convert to general form: 

Identify the x­intercepts and y­intercept from each equationThen check on graphing calculator.

y = 2(x ­ 1)(x + 1)(x ­ 2) 

x ­ ints: 

y ­ int: 

y = ­(x ­ 3)(x + 2)2

x ­ ints: 

y ­ int: 

1, ­1, 2 3, ­2(Double)

­(­3)(2)2 = 12

(0, 12)

2(­1)(1)(­2) = 4

(0, 4)

erasable

Double Root  Bounces

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor)

4. Convert to general form:  

1. Write equation using         x­intercepts

2. Plug in y­intercept

3. Solve for "a"

y = __(x + 3)(x ­ 4)

24 = a(3)(­4) = ­12a

a = ­2y = ­2(x + 3)(x ­ 4)

review ­ may skip for time

erasable

Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor)

4. Convert to general form:  

Write equation using          x­intercepts

Plug in y­intercept (0, ­2) & Solve for "a"

y = __(x + 4)(x + 1)(x ­ 2)

­2 = a(4)(1)(­2) ­2 = ­8a.25 = a

y = .25(x + 4)(x + 1)(x ­ 2)

erasable

OYO: On your own

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Factor to find the x intercepts. 

x2 ­ 16  x2 +16 (x ­ 4)(x + 4)

Roots: 4 & ­4

(x ­ 4i)(x + 4i)

Roots: 4i & ­4i

erasable

Write the factored form of each polynomial: REMEMBER TO SOLVE FOR "a" (stretch factor) Write equation using 

x­intercepts

Plug in y­intercept & solve for "a"

4. Convert to general form:  

SKIP Unless needed

may skip for time

erasable

y = __(x + 2.5)(x ­ 3.2)(x ­ 7.5)

­90 = a(2.5)(­3.2)(­7.5)­90 = 60aa = ­1.5

y = ­1.5(x + 2.5)(x ­ 3.2)(x ­ 7.5)

Unit 13 Day 2 Polynomials.notebook April 05, 2018

Homework: WS #2 in GC

I can find the x,y intercepts of a polynomial equation

I can convert from factored to general form

I can solve for the scale factor of a polynomial

How are you doing?

Unit 13 Day 2 Polynomials.notebook April 05, 2018