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51 Cards in this Set

  • Front
  • Back
A term is...
a mathematical expression added or subtracted to another mathematical expression.
Factors are...
mathematical expressions multiplied to other mathematical expressions.
A glorified one is...
a fraction where top and bottom are the same.
i =
the square root of -1.
i^2 =
-1
Proper Complex Number format
a + bi
To add or subtract with i...
gather like terms.
When multiplying with i...
remember that 1^2 = -1.
When dividing with i...
remember that i is a radical; don't leave radicals (incl. i) in a denominator.
The conjugate of a complex number is...
the same real and imaginary terms, but with a different sign between them.
When there is a complex sum or difference in a denominator...
multiply the fraction by a glorified one of its conjugate to remove the i from the denominator.
When squaring a binomial...
remember that you'll get a trinomial.
You know it's a polynomial when...
all exponents are non-negative integers.
The degree of a polynomial is...
the largest exponent you see when in descending powers form.
A polynomial of degree one is...
a linear equation, drawing a line.
A polynomial of degree two is...
a quadratic equation, drawing a parabola.
A polynomial of degree three is...
a cubic.
A polynomial of degree four is...
quartic.
A polynomial of degree five is...
quintic.
To write a quadratic that is in descending powers form in vertex form (h, k)...
complete the square on the terms with the variable.
To find the x-coordinate of a quadratic in descending powers form...
calculate b/(2a).
To find the y-coordinate of a quadratic in descending powers form...
calculate the x-coordinate, then plug this value of the variable through the function.
A quadratic opens up if...
the leading coefficient is positive.
A quadratic opens down if...
the leading coefficient is negative.
An extreme value is ...
the top of a hill or the bottom of a valley of the graph of a function.
Extreme points are called (in mathematicalese)...
extrema.
A single extreme point is called (in mathematicalese)...
an extremum.
The extremum of a quadratic is also called...
its vertex.
The vertex of a quadratic is called (in mathematicalese)...
its extremum.
The zeros of a function are where...
the curve crosses or touches the x-axis.
The x-intercepts of a graph are called...
zeros.
The y-intercepts of a graph are called...
the y-intercepts, NOT zeros.
Four ways to solve a quadratic are...
1. Factoring (zero product property)
2. taking the square root of both sides (you may need to complete the square first)
3. graphing (not always accurate)
4. using the quadratic formula.
To solve a quadratic inequality...
first make distributions and combine like terms. Move all to the side where the quadratic term will be positive. Then decide where (in terms of x) the curve is above, on, or below the x-axis.
A polynomial function that has end behavior down to the left and up to the right...
is an odd-degree polynomial with a positive leading coefficient.
A polynomial function that has end behavior up to the left and down to the right...
is an odd-degree polynomial function with a negative leading coefficient.
A polynomial function that has end behavior up to the left and up to the right...
is an even-degree polynomial function with a positive leading coefficient.
A polynomial function that has end behavior down to the left and down to the right...
is an even-degree polynomial function with a negative leading coefficient.
A polynomial function may have extrema (turning points) equal in number to...
one less than its degree.
Polynomial functions may have as many zeros as...
the degree of the polynomial.
Polynomial functions with an odd degree must have [how many] zeros?
at least one
A comprehensive graph shows...
1) all x-intercepts, 2) the y-intercept, 3) all extrema (if any), 4) end behavior.
The Intermediate Value Theorem means...
that, if in a table of a polynomial function showing ascending or descending x-values, if the sign on the y-value changes then there is a zero between those two x-values.
Remainder Theorem...
If a polynomial P(x) is divided by (x - k), the remainder is equal to the value of the function where x = k. The point (k, remainder) is on the graph.
Functions have zeros, but equations have...
solutions.
The Conjugate Zeros Theorem says...
If a + bi is a zero of a polynomial, then so is a - bi.
Given a polynomial function and one of its zeros, find other zeros by...
using synthetic division to break apart the polynomial into factors.
A multiplicity of zeros means...
that a particular factor shows up more than once.
An odd multiplicity of zeros means the graph will...
cross the x-axis at that zero.
An even multiplicity of zeros means the graph will...
touch but not cross the x-axis at that zero.
The rational zeros theorem says...
If a polynomial has rational zeros, they may be found using (factors of the constant term) / (factors of the leading coefficient).