Unit 2 Review

Connecting Quadratics

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.

200

Convert the following Standard form Equation into its Factored form Equation

y=x^2-10x-24

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

300

Convert the following equation from Standard form to Vertex form:

y=x^2-10x+16

y = (x-5)^2-9

400

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

Standard form:

y=x^2-8x+12

Factored form:

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

Vertex form: 

y=(x-4)^2-4

500

y = 2x^2+12x+12

Convert the following equation from Standard form to Vertex form

y = 2(x+3)^2-6

Polynomials in the Short/Long Run

100

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

y=x^8+2x^7+3x^6+4x^5+5x^4+6x^3

Degree: 8

Lead Coefficient: 1

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

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

400

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

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

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+1.414t3−19.777t2+118.696t−205.332

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

FTA/Complex Roots

100

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

y=x^10-x^4-5x^3+11x^11-1

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

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

300

-sqrt(34)+4,567i

Find the Conjugate of the following term

-sqrt(34)-4,567i

400

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

Simplify the following terms by multiplication

34

500

Find the complex roots of the following quadratic:

T(x)=x^2+4x+5

-2 + i and -2-i

Rational Functions

100

Find the horizontal asymptote of the following rational function:

y = (3x^2+4x+2)/(4x-1

there is no horizontal asymptote!

200

Find the horizontal asymptote of the following rational function:

g(x) = (2x+3x^2-1)/(3x+4-3x^2

y = -1

300

Factor the following rational function:

y=((x^2+12x+36))/(x^2-3x-28

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

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

List any zeros the rational function has:

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

There is a zero at (-5,0)