they look like this 0 zeros. what are zeros? zeros are what x equals or where your graph touches...

THEY LOOK LIKE THIS 0 Zeros

Upload: bethanie-bond

Post on 21-Jan-2016

213 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

THEY LOOK LIKE THIS 0

Zeros

What are zeros?

Zeros are what x equals

Where your graph touches the x-axis

How to Find Zeros

1. If you have a graph, look at it.

Wherever the graph crosses the x-axis, those are your zeros.

Page 4: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

2. If you have no graph and a simple equation like this:

-2x+4=0

Just solve.

Page 5: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

-2x+4=0 -4

-2x=-4 /-2

x=-4/-2x=2

Page 6: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

3. If you have a quadratic equation like this:

x = -2x2 - 6x + 8 = 0

No need to fear.

Just factor.

Page 7: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

x = -2x2 - 6x + 8 = 0

becomes

(-2x-7)(x-1)=0

Set each one equal to 0 and solve

Page 8: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

-2x-7=0 +7

-2x=7 /-2

x=7/-2

x-1=0 +1

x=1

x=7/-2, x=1

Page 9: THEY LOOK LIKE THIS 0 Zeros. What are zeros? Zeros are what x equals OR Where your graph touches the x-axis

What if factoring doesn't work?!?!

Don't worry. It's okay.

Use the quadratic formula.

-b +/- (square root)b2-4ac/2a

Factoring or writing a polynomial as a product can be useful for finding the x-intercepts or zeros. Solving a quadratic equation means finding the zeros

Warm-up7.1 1)What are the zeros of the function : y = x 3 – 4x 2 + x + 6? 2)What is the discriminant of 2x 2 – 5x + 4=0? 3)What is the end behavior of

Section 2-3 Real Zeros of Polynomial Functions. Real Zeros of Polynomial Functions What you should know: 1. How to divide polynomials by other polynomials

math1005postexam2reviewsolnF13 (1) Page 1quick049/Postexam2ReviewKEY.pdf5. Use the rational zeros theorem to determine the potential rational zeros Of the polynomial function f(x)

Roots & Zeros of Polynomials How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related. 2.5 Zeros of Polynomial Functions

pquinn.cmswiki.wikispaces.netpquinn.cmswiki.wikispaces.net/file/view/Quinn_MathIII_Review.pdf · Example 2: Find the inverse 9Cf(x) = values switched. ... What are the zeros of the

Polynomial P(x) Binomial Factors Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)

unit2studyguide - Math with Ms. BaskinExample 2: State the number of possible real zeros and turning points off(x) = x3 + 2x2 —x — 2. Then determine all of the real zeros by factoring

5.6 Find Rational Zeros - Moore Public Schools · Find all real zeros of the function. 12. f(x) = x3 5x2 22x + 56 14. h(x) = x3 + 8x2 9x 72 Find all real zeros of the function. Use

polynomial function...Zeros of a Polynomial Function in Quadratic Form State the number of possible real zeros and turning points for h (x) = x 4 – 4x 2 + 3. Then determine all of

Curso Técnico em Eletrotécnica - drb-m.org · Preto Marrom Vermelho Laranja Amarelo Verde Azul Nenhum zero 1 zero 2 zeros 3 zeros 4 zeros 5 zeros 6 zeros As cores violeta, cinza

Nonminimum-Phase Zeros - University of Michigandsbaero/others/Hoag...What exactly do zeros do, and how do zeros relate to the number zero? A zero of a transfer function is a root of

R ZEROS Frequently Asked Questions · ZEROS Frequently Asked Questions System Characteristics What is ZEROS? ZEROS (Zero-emission Energy Recycling Oxidation System) is an “oxy-fuel”

Newton’s Method finds Zeros Efficiently finds Zeros of an equation: –Solves f(x)=0 Why do we care?

Section 2.5 Zeros of Polynomial Functions of Polynomial... · Section 2.5 Zeros of Polynomial Functions The Rational Zero Theorem Example List all possible rational zeros of f(x)=x3-3x2-4x+12

Barrelet zeros

3.4. ZEROS OF POLYNOMIAL FUNCTIONSPossible rational zeros: ±1, ±2, ±3, ±6 Solution By applying synthetic division successively, you can determine that x = –1 and x = 2 are the

Splash Screen. Concept Example 1 Identify Possible Zeros A. List all of the possible rational zeros of f(x) = 3x 4 – x 3 + 4. Answer:

“Parabola and Your Life” Quadratic Functions. The Zeros of Quadratic Functions The zeros of Quadratic Function f(x) = ax 2 + bx + c can be found by letting

ZEROS OF ORTHOGONAL POLYNOMIALS GENERATED · ZEROS OF ORTHOGONAL POLYNOMIALS GENERATED ... (x−c) dµ(x)+Nδ ... sharp bounds and speed of convergence to them for their

Find the zeros of the following function F(x) = x 2 -1 Factor the following function X 2 + x – 2 Simplify the expression: X 2 + x – 2 x 2 – x – 6

X-intercept Roots Zeros Hits ground/water ~= 0 Crosses x-axis (~,0)

ZEROS=ROOTS=SOLUTIONS Equals x intercepts Long Division 1. What do I multiply first term of divisor by to get first term of dividend? 2. Multiply entire

Roots, Zeros, Axis of Vertex: x-interceptsforrestermath.weebly.com/uploads/5/7/6/4/57643655/...Roots, Zeros, x-intercepts: NONE Vertex: (-1,1) a Minimum Axis of Symmetry: the line

Warm-up Jan. 27 HW: Finish midterm review packet & study. Midterm is tomorrow! 1.2. What are the zeros of the polynomial defined by the function y = x

3.3 - 1 3.3 Zero of Polynomial Functions Factor Theorem Rational Zeros Theorem Number of Zeros Conjugate Zeros Theorem Finding Zeros of a Polynomial Function

Função do 2ºGrauRaízes (zeros) da função do 2.º grau Para determinar as raízes (ou zeros) da função do 2º grau f(x) = ax2 + bx + c, basta calcular os valores de x que tem

NPS Learning in Place Algebra I...Use your knowledge of the relationships between x-intercepts, zeros, factors, and solution sets to complete the table below. Graph x-intercepts Zeros

What are you finding when you solve the quadratic formula? Where the graph crosses the x-axis Also known as: Zeros, Roots and X-intercepts

Splash Screen. Example 1 Identify Possible Zeros A. List all of the possible rational zeros of f(x) = 3x 4 – x 3 + 4. Answer:

ZEROS=ROOTS=SOLUTIONS Equals x intercepts. Another Memory slide

Loudoun County Public Schools€¦ · Find the rational zeros and put function in factored form: -1 (twice), 2; f(x) Find complex zeros: 2 ± i 3 List the zeros, including repeated

1) Find all the zeros of f(x) = x4 - 2 2x - 31x + 32x + 240. Find all the real zeros of the polynomial f(x) = x4 – x3 – 20x2 and determine the multiplicity of each

Zeros of p(x)

Alg 11 - 9.3 Graphing General Rational Functions Example 4: Graph y — a) Find the x-int (zeros of the numerator) x-int: b) Find the VERTICAL asymptotes (zeros of the denominator)