The polynomial projectDone by :Fatima Abdulla Alweshahi Sara saeed Alkaabi .11:51

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Polynomial This Way Presentations are a powerful communication medium.

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Task1

Task 2

Task 3

Task 4

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Task 1 : Find the polynomial that gives the following values

a. Write the system of equations in A, B, C, and D that you can use to find the desired polynomial.

10=A-6=A+B(x1-x0)-17=A+B(x2-x0)+(x2-x0) (x2-x1)82=A+B(x3-x0)+(x3-x0)(x3-x1)+D (x3-x0) (x3-x1)(x3-x2)For more than 20 years, Duarte has developed presentations4

Solve the system obtained from part a.

10 = A-6 = 10 + B (1-(-1) 2B = -16 B = -8-17= 10 + -8 ( 2-(-1)) + ((2 ( - 1) ( 2 1) 3(= - 3 (= - 182 =10+ -8 (5 ( - 1 )) + - 1 (5-(-1)) (5-1) +D (5-(-1)) (5-1) (5-2)72D = 144 D=2A=10 B= -8 (= - 1 D =2

c. Find the polynomial that represents the four ordered pairs.

P( x ) = 10 + -8 (x ( - 1 ) + - 1 (x ( - 1 )) ( x 1 ) +2) x ( - 1 )) ( x 1 ) ( x 2 ) =10 8 x - 8 x 2 + 1 + 2 (x3 2x2 x + 2 ) = 3 x 2 8 x + 2x3 4x2 2 x + 4 = 2 x 3 5 x 2 10 x + f.

D . Write the general form of the polynomial of degree 4 for 5 pairs of numbers.P (x) = A+B ( x x 0) + ( x x 0) ( x x 1) + D ( x x 0) ( x x 1 ) ( x x 2 ) + E ( x x 0 ) ( x x 1 ) ( x x 2) (x-x3) = E x 4 + ( 2 f E ) x 3 + (9 E 5 ) x 2 + (FE 10 ) x + (F 10 E )

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Task 2: Find the zeros of the polynomial found in task 1.

A . Show that the 3 zeros of the polynomial found in task 1 are:First zero lies between -2 and -1Second zero lies between 0 and 1Third zero lies between 3 and 4.

F ( - 2 ) = 1 , F ( - 1 ) = 10 mid point = - 1 . 5F (0) = F , F ( 1 ) = - 6 = 0 . 5 F ( 3 ) = - 14 , F (4) = 15 = 3 . 5

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B . Find to the nearest tenth the third zero using the Bisection Method for Approximating Real Zeros.

F (3) = - 14 , f (4) = 15 3 . 5 F ( 3 . 5 ) = - 3 . 5 mid point

F (3 . 5 ) = - 3 . 5 f ( 4) = 15 3 . 75 F ( 3 . 75 ) = 4 . 658 mid point

F ( 3 . 5 ) = 3. 5 f ( 3 .75 ) = 4 . 658 3 . 625 F ( 3 . 75 ) = 4 .658 mid point

F ( 3 . 5 ) = 3 . 5 f ( 3 . 75 ) = 4 . 658 3 . 625 F (3 . 625) = 0 . 319

F (3. 625 ) = 0 . 319 f ( 3 . 75 ) = 4 . 658 3 . 68f5F ( 3 . 68 f 5 ) = 2 . 42

F ( 3 . 68f 5 ) = 2 .42 f ( 3 . 75 ) = 4 658 3 . 718

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You are planning a rectangular garden. Its length is twice its width. You want a walkwayw feet wide around the garden. Let x be the width of the garden.A . Choose any value for the width of the walkway w that is less than 6 ft.W = 1 f t B . Write an expression for the area of the garden and walk.A = L x w = 2 w x w A=2x2ft2Parameter = 2 (( + w ) = 2 ( 2 x + x ) = 4 x + 2 x parameter = 6 x

Task 3: Real World Construction

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C . Write an expression for the area of the walkway only.

Parameter = 2 (( + w )= 2 (2 w + w )= 2 ( 3 w )= 2 ( 3 x )= 2 6 x f t D . You have enough gravel to cover 1000ft2 and want to use it all on the walk. Howbig should you make the garden?

1000 = 2 w 2 1000 = 2 x 2 500 = x 222 . 36f t =x L = x 2 = 2 x 22 . 36 L = 44 . 72 f t

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Task 4: Using Technology:a. Use a graphing program to graph the polynomial found in task 1

B . Make a PowerPoint to present your project and upload it on a wiki.http://mathproject121.wikispaces.com/

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Polynomials

A polynomial is made up of terms that are only added, subtracted or multiplied.

A polynomial looks like this:

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Polynomial comes form poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

A polynomial can have:constants (like 3, -20, or )variables (like x and y)exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etcand they can be combined using:+addition,-subtraction, andmultiplication ... but not division! Those rules keeps polynomials simple, so they are easy to work with!

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Polynomial or Not?

These are polynomials:3xx - 2-6y2 - (7/9)x3xyz + 3xy2z - 0.1xz - 200y + 0.5512v5+ 99w51

(Yes, even "1" is a polynomial, it has one term which just happens to be a constant).

For more than 20 years, Duarte has developed presentations13And these are not polynomials2/(x+2) is not, because dividing is not allowed1/x is not3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)x is not, because the exponent is "" (see fractional exponents)But these are allowed:x/2 is allowed, because it is also ()x (the coefficient is , or 0.5)also 3x/8 for the same reason (the coefficient is 3/8, or 0.375)2 is allowed, because it is a constant (= 1.4142...etc)

align employees, 14

There are special names for polynomials with 1, 2 or 3 terms:

global causes.15

MonomialThe first rule is: Treat your audience as king.16

Binomial2The second rule is: Spread ideas and move people.17Trinomial3

The next rule is: Help them see what you are saying.18

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Along the way weve discovered19

How do youremember thenames?Your audience deserves to be treated like royalty. Design a presentation that meets their needs, not just yours.20How do you remember the names? Think cycles!

Give them those things in a clear, easily understandable way21

Can Have Lots and Lots of TermsPolynomials can have as many terms as needed, but not an infinite number of terms.

You are not giving your presentation to have another meeting. You are there to covey meaning.22

So, consider including imagery that powerfully illustrates your point.23

What is Special About Polynomials?Because of the strict definition, polynomials are easy to work with.For example we know that:If you add polynomials you get a polynomialIf you multiply polynomials you get a polynomialSo you can do lots of additions and multiplications, and still have a polynomial as the result.Also, polynomials of one variable are easy to graph, as they have smooth and continuous lines.

Sometimes moving images can inspire in a way that static slides cannot. A slow moving animation creates a sense of nostalgia.24

A sequential build adds a sense of suspense.25

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

And a thought-provoking video moves your audience in a way that can change not only minds, but hearts.26

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

You don't have to use Standard Form, but it helps.

And a thought-provoking video moves your audience in a way that can change not only minds, but hearts.27