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Quadratic Functions
Complex Numbers
Polynomials
Solutions of Polynomial Functions
Rational Functions
100

The coordinates of the vertex of 

f(x) = -0.5x2 - 2x - 5.

What is (-2, -3)?

100

(2+3i)+(−8+i)

What is −6+4i?

100

What is the end behavior of the polynomial?

f(x)=10x2−23x+50

x→−∞,f(x)→∞

x→∞,f(x)→∞

100

How many zeros does the polynomial have?

f(x)=2x5+4x3−8x2

What is 5?

100

Determine the vertical asymptotes and holes (removable points of discontinuity) of the rational function shown below.


f(x)=(x−1)(x−2) / (x−1)(x+7)

Holes at x=1

Vertical Asym. at x=-7

200

The number of pianos produced and sold that will maximize the profit of 

P(x) = -1.5x2+5100x +6000, where x is the number of pianos produced and sold and P(x) is the profit, in dollars.

What is 1700 pianos?

200

(12−3i)−(5−4i)

What is 7 + i?

200

Find the degree, leading term, leading coefficient, constant term, and end behavior of the given polynomial.

g(x)=−2x2+5x9−3x+6

What is 9?

What is 5x9?

What is 5?

What is 6?

x→−∞,g(x)→-∞

x→∞,g(x)→∞

200

List the possible rational roots of:

f(x)=x3+6x2−9x−14

What is ±1,±2,±7,±14 ?

200

Find the domain of the given function. Enter the solution using interval notation.

f(x)= x+8 / x2−9x−10

what is (−∞,−1)∪(−1,10)∪(10,∞) ?

300

describe the transformations that take place on f(x)=x2 to get

g(x)=4(x+7)2 -2

What is Shift left 7 units
Shift down 2 units
Vertical stretch by a factor of 4?

300

√−50

What is 5i√2?

300

Identify the zeros of f(x)=−(x+10)(x+2)2(x−9) and their multiplicity. (Smallest to Largest)

x=-10  mul. 1

x=-2  mul. 2

x=9  mul. 1

300

Is x+2 a factor of the polynomial?

f(x)=x4+10x3−24x2+20x+44

No; f(-2) = -156

300

Find the horizontal asymptote or oblique asymptote.  

f(x)= (−3x+3x3−4) / (−x3+x2+5)

Horizontal Asym. at y=-3

400

The maximum revenue, in dollars, where x is the price of each hot dogs if 

R(x) = -100x2+600x+1500.

What is $2400?

400

(3−2i)(5+4i)

What is 23+2i?

400

Divide 2x4−6x3−12x2+15x+4 by x−4

(answer will be in quotient)

What is 2x3+2x2−4x−1?

400

If (x-4) is a factor of

f(x)=x3+4x2−25x−28

find the remaining zeros to rewrite in factored form

What is (x−4)(x+1)(x+7) ?

400

Find the horizontal asymptote or oblique asymptote. 

 f(x)= (x2+6x+3) / (x+2)

What is y= x+4 ?
500

Function:  y=(x+1)2 −1

Does the parabola open up or down?   

Vertex (x,y)=

Equation of the Axis of Symmetry:

What is up?

What is (-1,-1)?

What is x=-1?

500

Divide

3+4i / 7−i

(17+31i)/50

500

Divide

2x3−2x2−21x−19 by x+2

2x2−6x−9+(−1/x+2)


500

Find all zeros of the polynomial:

f(x)=x3+6x2−9x−14

x=−1,−7,2

500

Let f(x)= (x2−2x−8) / (x2−4x−12)

Find:

a) Domain (interval notation)

b) Hole(s) at x=

c) Vertical asy. at x=

d) Horizontal asy. at y=

a)  (−∞,−2)∪(−2,6)∪(6,∞)

b) x=-2

c) x=6

d) y=1