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Graphs
Leading Coefficient Test
Vocabulary
Division
Complex Numbers
100
A parent function can undergo _________ (amount) transformations.
What is infinitely many?
100
The leading coefficient test can be used as long as the leading coefficient (a sub n) is not equal to ________.
What is zero?
100
A _______________ is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.
What is a complex number?
100
The binomial x-k is a factor of the polynomial f(x) if and only if f(k)=______.
What is zero?
100
Simplify (13+i)-(4-i).
What is 9+2i?
200
The _________________ of any parabola is given by x = -b/2a.
What is axis of symmetry?
200
If the degree, n , is even and the leading coefficient is negative then the graph _______ on the left and ______ on the right.
What is falls and falls?
200
3 + i and 3 - i are called _________________.
What is complex conjugates?
200
Determine if x-1 is a factor of x^3 - 1?
What is yes?
200
Multiply 8-i with its conjugate.
What is 65?
300
The x-intercepts of 2x(x-2)(x+4)=0 are _________.
What is 0, 2, and -4?
300
Give the equation of a function that rises on the left and right.
What is (check equation--> n must be even and LC must be positive)?
300
___________________ can only be used when the divisor is in the form of x - k.
What is synthetic division?
300
Find the remainder of 2x^3 -7x^2 +5 divided by x-3.
What is negative four?
300
Simplify 3(2i)(5i)^2?
What is -150i?
400
A quadratic function that is NOT ____________ will not have any real x-intercepts.
What is factorable?
400
Give the equation of a polynomial function with at least 4 turning points that falls on the left and rises on the right.
What is (positive LC)x^5 ....?
400
The Leading Coefficient Test is the test which enables you to discover the behavior of the graph in terms of _____ and ______.
What is rising and falling?
400
Divide 27x^3 + 64 by 3x+4.
What is 9x^2 -12x + 16?
400
True or False: 101 is a complex number.
What is 101 + 0i?
500
The vertex of 3x^2 - 6x + 5 is (__,__).
What is (1,2)?
500
Use the LC Test to sketch the graph of f(x)=x^3 + 3x^2 -x - 3 (include zeros).
What is (check graph)? falls on left/rises on right and zeros:-1,1,-3
500
In mathematics, a _____, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x) = 0. In other words, it is an input value that produces an output of zero (0).
What is a zero?
500
Use long division to find the quotient and remainder when 2x^4 -x^3 -2 is divided by 2x^2+x+1.
What is x^2 - x (quotient) and x-2 (remainder)?
500
Multiply (a+bi)(c+di). Write solution as a complex number.
What is (ac-bd)+(ad+bc)i?