M3D13 Have out: Bellwork: pencil, red pen, highlighter, notebook

Slides:



Advertisements
Similar presentations
“ARE YOU READY FOR THIS?”. 1. Classify this polynomial by degree: f(x) = 4x³ + 2x² - 3x + 7 a. binomial b. 4 term c. cubic d. quartic How do you know?
Advertisements

Quadratic Equations From Their Solutions From solutions to factors to final equations (10.3)
4.2-2 Constructing Polynomial Functions. Now, we have learned about several properties for polynomial functions – Finding y-intercepts – Finding x-intercepts.
Lesson 7.7.  Polynomials with degree 3 or higher are called higher-degree polynomials.  If you create a box by removing small squares of side length.
Polynomials and Rational Functions (2.1)
Graphing polynomials To graph a polynomial we need to know three things 1) Type of polynomial 2) Roots 3) y-intercept.
Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:
A Library of Parent Functions Objective: To identify the graphs of several parent functions.
Accelerated Math II Polynomial Review. Quick Practice “Quiz” 1. A rectangular sheet of metal 36 inches wide is to be made into a trough by turning up.
5.5 Theorems about Roots of Polynomial Equations P
Evaluate and graph polynomial functions. GOALS: “” Algebra 2: Notes 5.2: End Behavior of Polynomials: Zeros of Polynomials: If P is a polynomial and if.
The sum or difference of monomial functions. (Exponents are non-negative.) f(x) = a n x n + a n-1 x n-1 + … + a 0 Degree of the polynomial is the degree.
5.2 Polynomials, Linear Factors, and Zeros P
Warm Up Are the following graphs even or odd? (Draw them on your paper) 2.What are the zeros for the given polynomial function and what is the multiplicity.
A rational function is a quotient of two polynomials: where and are polynomials of degree n and m respectively. Most questions about a rational function.
2.3 Real and Non Real Roots of a Polynomial Polynomial Identities Secondary Math 3.
6-5 & 6-6 Finding All Roots of Polynomial Equations Warm Up: Factor each expression completely. 1. 2y 3 + 4y 2 – x 4 – 6x 2 – : Use factoring.
Section 4.6 Complex Zeros; Fundamental Theorem of Algebra.
Graphing polynomials To graph a polynomial we need to know three things 1) Type of polynomial 2) Roots 3) y-intercept.
Section 4.2 Graphing Polynomial Functions Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:
Standard Form Objective: To graph the equation of a line in Standard Form from give information. Warm – up: Write the following equations in Standard Form.
Goal: Solve quadratic equation by factoring the trinomial. Eligible Content: A
PreCalculus 4-R Unit 4 Polynomial and Rational Functions Review Problems.
PreCalculus 2-R Unit 2 Polynomial and Rational Functions.
WARM - UP 1.Given the following information sketch a graph of the polynomial: 2.Find all of the roots of the following polynomial:
Chapter Polynomials of Higher Degree
Polynomial Function Review
Where am I now? Review for quiz 4.1.
DAILY CHECK Complex roots.
Roots and Zeros 5.7.
When solving #30 and #34 on page 156, you must “complete the square.”
Polynomial Functions.
Lesson 7.2: Finding Complex Solutions of Polynomial Equations
4.2 Properties of Polynomial Graphs
**Get signed by your parents for 5 bonus points on the test!!
(These will be on tomorrow’s quiz!)
3.4 Zeros of Polynomial Functions: Real, Rational, and Complex
10/19 Staple pages 244,245,249,250,255 together. Put your name on it.
5-Minute Check Lesson 4-1.
Assignment, pencil, red pen, highlighter, textbook, notebook, graphing calculator U4D6 Have out: Bellwork: Write the equation in Vertex form by completing.
Jeopardy Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200
4.3: Polynomial Functions
Assignment, pencil red pen, highlighter, GP notebook, graphing calculator U4D7 Have out: Bellwork: Graph each function on the same set of axes. Be sure.
Solving Polynomial Functions
Work on the first page of today’s packet.
Fundamental Thm. Of Algebra
Pencil, highlighter, red pen, calculator
M3D7 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
Work on example #1 in today’s packet.
Have out: U1D6 Bellwork: a) x2 + 10x + 24 b) x3 – 4x2 – 45x
Daily Checks From Yesterday!
M3D12 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
Assignment, pencil red pen, highlighter, GP notebook, graphing calculator U4D8 Have out: Graph the function and its asymptotes, then identify.
Preview to 6.7: Graphs of Polynomial
U7D15 Have out: Bellwork: Pencil, red pen, highlighter, notebook
U7D9 Have out: Bellwork: pencil, red pen, highlighter, notebook
U7D8 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
U7D3 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
Assignment, red pen, pencil, highlighter, GP notebook
U7D14 Have out: Bellwork: Pencil, red pen, highlighter, notebook
M3D16 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
M3D11 Have out: Bellwork: x – 4 x2 + 4x + 42 x + 2y x2 – 2xy + (2y)2
U7D4 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
Assignment, red pen, pencil, highlighter, GP notebook
M3D10 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
M3D17 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
U7D7 Have out: Bellwork: x – 4 x2 + 4x + 42 x + 2y x2 – 2xy + (2y)2
M3D14 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
U7D13 Have out: Bellwork: pencil, red pen, highlighter, GP notebook
Presentation transcript:

M3D13 Have out: Bellwork: pencil, red pen, highlighter, notebook Complete #1a on the handout. 1) Determine all the zeros and sketch the graph of y = P(x). Label all intercepts. y a) Degree: ___ Zeros: ____________ x Remember: Only graph the real zeros, and make sure the graph fits the criteria that is known for sure.

Any other possibilities out there? 4 Degree: ___ Zeros: ____________ y x (–2,0) (2,0) What are the criteria we know? (1) x–intercepts (0, –100) (2) y–intercept (3) end behavior Any other possibilities out there? Draw a 4th degree polynomial that fits these criteria.

3 b) Degree: ___ Zeros: ____________ End behavior: y (0,0) x (7,0) (–7,0) (7,0) End behavior:

Any other possibilities out there? c) 4 Degree: ___ Zeros: ____________ y x (–2,0) (2,0) What are the criteria we know? (1) x–intercepts (2) y–intercept (0, –36) (3) end behavior Any other possibilities out there? Draw a 4th degree polynomial that fits these criteria.

d) 3 Degree: ___ Zeros: ____________ End behavior: y (0, 8) x (–4,0) End behavior: Be sure to put an inflection point somewhere.

e) 4 Degree: ___ Zeros: ____________ End behavior: y (0, 25) (–1,0) (1,0) x (–5,0) (5,0) End behavior:

f) 5 Degree: ___ Zeros: ____________ End behavior: y (0,0) x (4,0) (–3,0) (4,0) End behavior:

Remember: When there is a complex zero there is always a _____________. conjugate pair For instance: –5i is paired up with +5i. (9 + 4i) is paired up with (9 – 4i).

Part 2: Find a standard (expanded) form equation of a polynomial with the given zeros. a) cubic polynomial with zeros x = 2 and i. There must be a conjugate pair to i : –i So there are 3 zeros: x = 2, ±i x = 2 Any time you see a “±” you have to square both sides. x – 2 = 0 Expand using F.O.I.L. or a generic rectangle. Note: We are finding “a polynomial”, so you do not need to find a specific leading coefficient, “a”.

b) quartic polynomial with zeros x = 3 and degree: 4 All the zeros are: Any time you see a “±” you have to square both sides. Expand using F.O.I.L. or a generic rectangle. Check: This is degree is 4!

c) quartic polynomial with zeros x = 4i and degree: 4 2 zeros here. There has to be two zeros here. Expand using F.O.I.L. or a generic rectangle. Check: This is degree is 4.

d) 5th degree polynomial with zeros x = 1, i, 2i. one real zero 2 zeros 2 zeros Expand using generic rectangles Yep, it’s degree 5! Here is a link to check something like this: poly expand link

Complete the worksheet.

Determine the polynomial function P(x) Determine the polynomial function P(x). Write your answers in factored form. –1, –1, 3 a) zeros: __________ y P(x) = a (x + 1)2 (x – 3) 4 = a(–2 + 1)2(–2 – 3) 4 = a(–1)2(–5) (–2, 4) 4 = a(1)(–5) 4 = –5a x

Determine the polynomial function P(x) Determine the polynomial function P(x). Write your answers in factored form. –4, –1, 3, 3 b) y zeros: _____________ (1, 5) P(x) = a (x +4) (x +1) (x – 3)2 5 = a(1 + 4)(1 + 1)(1 – 3)2 x 5 = a(5)(2)(–2)2 5 = a(5)(2)(4) 5 = 40a