Half Test Review! Day 6.

Slides:



Advertisements
Similar presentations
$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.
Advertisements

Example 4 Solving a Quartic Equation Chapter 6.4 Solve the equation.  2009 PBLPathways.
The Quadratic Function A Quadratic function is a function of the form where a, b and c are real numbers and.
EXAMPLE 2 Find the zeros of a polynomial function
EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial function.
Section 3-5 Finding Real Roots of Polynomial Equations
3-5 Finding the real roots of polynomial Equations
CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.
Role of Zero in Factoring
Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function.
GUIDED PRACTICE for Example How many solutions does the equation
EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. – – 8 5 – 6 15 – 21 2 – 5 7 – 16 2x 3 + x 2.
Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.
Objectives Identify the multiplicity of roots Use the Rational Root Theorem and the Irrational Root Theorem to solve polynomial equations.
Ch 2.5: The Fundamental Theorem of Algebra
Polynomials and other functions. Graphing Polynomials Can you find the end behavior? Can you identify the zeros, roots, x-intercepts, or solutions? Can.
1. Describe the end behavior of the graph y = 2x 5 – 3x Sketch a graph of 3 rd degree with a zero at -5 (multiplicity 2) and a zero at 0 (multiplicity.
Complex Numbers, Division of Polynomials & Roots.
Objective: Students will be able to use the rational root theorem and the irrational root theorem to solve polynomial equations, and can identify the multiplicity.
HA2 Ch. 5 Review PolynomialsAnd Polynomial Functions.
7.3 Products and Factors of Polynomials Objectives: Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.
Warm Up 1.What is the absolute minimum of f(x) = 2x 4 – 17x x 2 – 7x – 15 2.A ball is thrown into the air. It’s height above the ground in feet is.
Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.
1. Describe the end behavior of the graph y = 2x 5 – 3x Sketch a graph of 3 rd degree with a zero at -5 (multiplicity 2) and a zero at 0 (multiplicity.
SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.
Section 3-6 Fundamental Theorem of Algebra
Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =
Warm UpMar. 5 th 1.What is the absolute minimum of f(x) = 2x 4 – 17x x 2 – 7x – 15 2.A ball is thrown into the air. It’s height above the ground.
Finding Real Roots of Polynomial Equations 3-5
LESSON 5.6 Rational Zeros of Polynomial Functions.
Chapter 6 – Polynomials and Polynomial Functions 6.6 –Polynomials of Greater Degree.
Factor completely. 1. x2 – x – 12 ANSWER (x – 4)(x + 3)
Algebra II Review. Question 1: Which of these are all of the zeros of x 3 + x 2 – 2x – 2 = 0 1.1, –1 2.–1 3.–1, √2 4.1, √2 5.1, ±√2 6.–1, ±√2.
5.2 Polynomials, Linear Factors, and Zeros
Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.
SLO Review Warm Ups. Warm Up 4/24/15 1.Identify the roots of the equation. State the multiplicity at each root. (Graph to find a root, then use synthetic.
DIVIDING POLYNOMIALS REMAINDER AND FACTOR THEOREMS FINDING ZEROS FOR POLYNOMIALS Section 2.5 – 2.7.
Remainder Theorem Section 6-3b. Remainder Theorem.
Find the roots Identify the multiplicity 3.5: Finding Real Roots of Polynomial Equations.
Holt McDougal Algebra Fundamental Theorem of Algebra Intelligence is knowing that a tomato is a fruit; Wisdom is not putting it in a fruit salad.
Lesson 6-3: Dividing Polynomials
6.3 Dividing polynomials.
Warm Ups Term 2 Week 6.
Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)
Warm up Factor the expression.
Please log on to your computers.
Name:__________ warm-up 5-8
When given a root and when not given a root
10.4 Solving Factored Polynomial Equations
Solving Polynomial Functions
Warm Up Identify all the real roots of each equation.
Warm Up Identify all the real roots of each equation.
Apply the Remainder and Factor Theorems
1 Describe the vertical and/or horizontal 
translations of the graph f(x) = x2 or f(x) = |x| b) a)
Unit 7 Day 4 the Quadratic Formula.
**Get signed by your parents for 5 bonus points on the test!!
Apply the Fundamental Theorem of Algebra
Warm-Up 5 minutes Solve by completing the square. 1) x2 – 10x + 23 = 0
Chapter 2 notes from powerpoints
Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)
Solving Special Cases.
Warm Up The area of a rectangle is expressed by the polynomial
Warm Up: Put on the back of guided notes
Warm UP: Factor Completely: 1)16n3 + 32n2 – n – 2 2) y4 – 3y2 – 28
Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER
2.6 Find Rational Zeros Pg. 89.
Solving Polynomial Equations
Solving Special Cases.
2.6 Find Rational Zeros Pg. 89.
3.2 The Remainder Theorem.
Presentation transcript:

Half Test Review! Day 6

Warm-up 1. State the zeros and multiplicity for the equation y = (x + 5)2(3x + 9)5 2. (x4 + x3 – 1) ÷ (x – 2) Factor: 2x3 + 10x2 + 12x What is the end behavior of the polynomial in #3?

Homework Answers: Packet Page 7 #1-7 How did you do?

More Review problems!! 1. Divide using synthetic division: (2x3 + 3x2 -8x + 3) ÷ (x + 3) State the zeros and multiplicity of (x -7)4(5x + 25) 3. Name by degree and number of terms: f(x) = 5x5 – 2x3 + 4x2

More Review problems!! 4. The volume in cubic feet of a box can be expressed as V(x) = -x3 – x2 + 6x. The depth is expressed as 2 – x. Assume that the height is greater than the width. Find the linear expressions for the height and the width.

More Review problems!! Write the equation in factored form. State the degree!!

Review for Mastery 1. 2. Graph and state the domain and range of y = -x3 + 7 3. What is the value of the determinant when x= 2 and y = 3

Review for Mastery 4. Solve: 9y + 2z = 18 3x + 2y + z = 5 X – y = -1 5. Solve:

Review for Mastery 6. Find the value of the discriminant and state the number and type of solutions. y = 3x2 + 4x + 5 7. Set the function in #6 equal to zero and solve using the quadratic formula.

Work on your mastery test review guide!!!