Quadratic Functions and Models
Synthetic Division
Zeros of Polynomial Functions
Rational Functions
Potpourri
100
This is the graph of f(x)=x^2+2x-5 by completing the square to find the vertex.
What is: Vertex(-1,-6)
f(x)=(x+1)^2-6
100
When using Synthetic Division, this is the degree of the divisor.
What is 1
100
These are all the zeros of the following polynomial given that 1-i is a zero.
What are
1-i, 1+i, 2, and 3
100
If f(x) is a rational function in reduced form, and for a real numbers a, this is the characteristic of what asymptote?
|f(x)| -> oo as x->a
What is a vertical asymptote
100
Descartes' rule of signs can be used to determine the number of positive and negative real zeros of
f(x)=2x^5-x^4+x^3-x^2+x+5
What is: Positive: 4, 2,, or 0.
Negative: 1
200
This is the vertex of a parabola from the Vertex Formula:
What is
(-b/(2a),f(-b/2a))
200
This is the difference between long division by x-c and synthetic division by x-c
What is Synthetic division: divide by c rather than (x-c) and add rather than subtract.
200
This is a polynomial function of least degree having only real coefficients and zeros 3 and 2+i
What is
f(x)=x^3-7x^2+17x-15
200
This condition must exist with a rational function for there to be a slant (oblique) asymptote.
What is "the degree of the numerator must be one greater than the degree of the denominator".
200
This is the theory that can be used to place upper and lower bounds on possible real zeros through which part of the synthetic division process.
What is the boundedness theorem and the bottom row of the synthetic division process.
300
The number of mosquitos, M(x), in millions, in a certain area if Florida depends on the June rainfall, x in inches. The function that models this phenomenon is M(x)=10-x^2. Find the amount of rainfall that will maximize the number of mosquitos.
What is 5 inches.
300
This is the verbal statement of the Remainder Theorem
What is "If the polynomial f(x) is divided by x-k, then the remainder is equal to f(k)
300
Given that i is a zero of f(x)=x^4+10x^3+27x^2+10x+26 , the answer is all the others.
What is
-5+i, -5-i
300
When a zero has an odd multiplicity > 1, the graph of the function does this at that zero?
What is wiggles
300
This is the sign of the leading coefficient and the (odd/even) of the power of the leading coefficient that would produce the following graph.
What is negative coefficient, even power
400
A ball is thrown directly upward from an initial height of100 ft. with an initial velocity of 80 ft. per sec. After how many seconds does the ball reach its maximum height?
What is 2.5 seconds
400
This is the solution to f(-2+i) for the function f(x)=x^3-4x^2+2x-29i
What is -18
400
This is all the complex zeros of 2x^4-x^3+7x^2-4x-4 given that 1 and -2i are zeros.
What is
1,-1/2,+-2i
400
This function can have a minimum of this degree according to its graph.
What is 5
400
Given that -4 and -1 are zeros of the following function, factor the function completely.
f(x)=x^4-3x^3-21x^2+43x+60
What is
(x+4)(x+1)(x-3)(x-5)
500
Mr. Harris has a taco stand. He has found that his daily costs are approximated by the function below. Find the number of units of tacos he should sell to mimimize his costs. What is the minimum cost?
C(x)=x^2-40x+610
What is 20 units; $210
500
The is the answer to: is x+4 a factor of f(x)=x^5+6x^4+11x^3+12x^2+5x-20
What is no
500
This is all the complex zeros of the following polynomial:
f(x)=x^4+x^3-9x^2+11x-4
What is 1,1,1,-4
500
This is the graph of the function f(x)=(x-5)/(x+3)
What is 
500
A rectangular region is enclosed by 180m of fencing. No fencing is needed along one side. This is the maximum area that can be enclosed.
What is 90m x 45m