200 300 100 300 100 200 300 100 200 300 100 200 300 100 Theorems I LOVE Parametric Equations...

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200 300 100 300 100 200 300 100 200 300 100 200 300 100 Theorems I LOVE Parametric Equations Factors, Remainders, And Roots (oh my!) Max-Min Inequalities Graph It 100 200 300 Misc. 100 200 300 200

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Transcript of 200 300 100 300 100 200 300 100 200 300 100 200 300 100 Theorems I LOVE Parametric Equations...

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TheoremsI LOVE

ParametricEquations

Factors, Remainders,

And Roots(oh my!)

Max-Min Inequalities Graph It

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Misc.

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How many real roots must an odd degree

polynomial have to have in order to have real

coefficients?

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1

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If a polynomial with real coefficients has a factor (x-(1-2i)), what must one of the other factors be?

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(x-(1+2i))

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The rational root theorem tells us that if a polynomial

has a root of the equation

then p must be what? p

xq

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A nonzero interger factor of the constant

coefficient

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Parameterize this equation:

3 5 6y x x

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3

( )

( ) 5 6

x t t

y t t t

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Find an equivalent equation without the

parameter t:

2

( ) 1

( ) 4

x t t

y t t t

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2

2

( 1) 4( 1)

6 5

y x x

y x x

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Find the domain and range for x-y equation, given the

following parametric equation

42

4)(

2)(

t

tty

ttx

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}82|{:

}84|{:

yyR

xxD

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Factor x3 + 6x2 - 4x - 24

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(x-2)(x+2)(x+6)

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What is the remainder What is the remainder when P(x)=xwhen P(x)=x200200+1 is +1 is

divided by x?divided by x?

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Is x = -0.5 a root of the Is x = -0.5 a root of the polynomialpolynomial

P(x) = xP(x) = x4 4 + 9.5x+ 9.5x3 3 - 7.5x- 7.5x2 2 - 26x - 10- 26x - 10??

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YESYES

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Two numbers add to 5. What is the largest

possible value of their product?

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6.25

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Suppose an area of farmland along a straight stone wall is

to be fenced. There are 400m of fencing available.

What is the greatest rectangular area that can be

enclosed?

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20,000m2

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An open box is to be made from a 3 foot by 8 foot piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the

box can have.

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~7.41ft3

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Solve | 2x + 3 | < 6

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-4.5 < x < 1.5(-4.5,1.5)

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Solve x2 + 2 ≥ 3x

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x ≤ 1 or x ≥ 2(1, 2)’

(-∞,1]U[2, ∞)

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Solve

0)2(

)1(

x

x

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x < -2 or x > 1[-2, 1]’

(-∞,-2)U(1, ∞)

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Is the function in the graph even, odd, or neither?

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ODDODD

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What type of polynomial is this a graph of?

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QuinticQuintic

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How many real roots does this quintic have?

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ThreeThree

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Find the expanded quadratic polynomial

with real roots with 1+i as one root.

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x2+2x+2

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Given y-intercept = 3 and x-intercept = 2, write a linear

equation for the line in intercept form.

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132

yx

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TRUE or FALSE:

is a polynomial.( )P x x

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FALSE


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