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Connecting Quadratics
Polynomials in the Short/Long Run
FTA/Complex Roots
Rational Functions
100

Below you are given a picture of a quadratic, you must label the parts of the quadratic that have an arrow pointing to them.

100

What is the Lead Coefficient and Degree of the following polynomial:

y=x8+2x7+3x6+4x5+5x4+6x3

Degree: 8

Lead Coefficient: 1

100

By the Fundamental Theorem of Algebra, how many roots should the following equation have?

y=x10-x4-5x3+11x11-1

11, because the highest degree that the equation has is 11!

100

Find the horizontal asymptote of the following rational function:

y=3x2+4x+24x-1


there is no horizontal asymptote!

200

Convert the following Standard form Equation into its Factored form Equation

y=x2-10x-24

y=(x-12)(x+2)

200

Given the graph above, list the end behavior of the graph as:

x approaches infinity, f(x) approaches ____________

x approaches negative infinity, f(x) approaches ________

x approaches infinity, f(x) approaches infinity

x approaches negative infinity, f(x) approaches 

negative infinity

200

Using the Fundamental Theorem of Algebra, how many real roots and imgainary roots does this function have?

2 imaginary and 0 real, because the graph never touches the x axis

200

Find the horizontal asymptote of the following rational function:

g(x)=2x+3x2-13x+4-3x2

y = -1

300

Convert the following equation from Standard form to Vertex form:


y=x2-10x+16



y=(x-5)2-9

300

Given the function, list the zeros of the function, and their multiplicities

g(x)=x(x-3)5(x+3)(x+4)2

Zero at 0, with multiplicity 1

Zero at 3, with multiplicity 5

Zero at -3, with multiplicity 1

Zero at -4, with multiplicity 2

300

-34+4,567i

Find the Conjugate of the following term


-34-4,567i

300

Factor the following rational function:

y=(x2+12x+36)x2-3x-28

f(x)=(x+6)(x+6)(x-7)(x+4)

400

Write the equation of the line (in any 3 forms)



Standard form:

y=x2-8x+12

Factored form:

y=(x-2)(x-6)


Vertex form: 

y=(x-4)2-4

400

Given the graph below, write the equation to this graph in factored form

(x+3)(x+1)(x-4)

400

(-3+5i)(-3-5i)

Simplify the following terms by multiplication


34

400

y=(x+4)(x-3)(x+4)(x-4)

List any vertical asymptotes the rational function has:


There is a vertical asymptotes at x = 4

500

y=2x2+12x+12

Convert the following equation from Standard form to Vertex form

y=2(x+3)2-6

500

Given the equation below, list the end behaviors of the graph:

as x approaches infinity, f(x) approaches _______

as x approaches negative infinity, f(x) approaches______


R(t)=0.037t4+1.414t319.777t2+118.696t205.332

a negative lead coefficient and an even degree means:

as x approaches infinity, f(x) approaches negative infinity

as x approaches negative infinity, f(x) approaches negative infinity

500

Find the complex roots of the following quadratic:

T(x)=x2+4x+5

-2+iand-2-i

500

List any zeros the rational function has:

y=(x+5)(x-4)(x-3)(x-4)

There is a zero at (-5,0)