vocabulary Flashcards
how does a constant function look on a graph?
horizontal line
define quadratic
polynomial function with the highest exponent being 2
whats the shape of a quadratic called?
parabala
what are the 5 methods to solve a quadratic
factoring, graphing, formula, complete the square, square roots
define factoring
to write something out as multiplication
whats always the first step in factoring?
gcf
what do you need to have for factoring?
leading coefficient must be positive
define square
numbers that have a rational square root
what needs to be true for a variable to be squared
needs to have an even exponenet
define perfect cube
taking the cube root of something and getting a rational number
what to the exponents of veriables need to be to be considered a “perfect cube”
a multiple of 3
what does the index on a radical tell you?
tells you to what root the radicand is being taken, if no index, then its to the square root
what does the coefficent of a radical do?
you multiply this by the radical as you’re going
what does the radical in a radical do?
its the symbol that divides the radicand from the index and coefficent
what does the radicand do in a radical?
its the number being taken down by the index number
if a radical has an even index and an odd radicand, what happens?
the radical is undefined
what can we assume when using variables in radicals?
that its a real number
When do you need an absolute value bar on the coefficient of a radical?
When theres an even index, original problem has an even exponent (under radical), and if theres an odd exponent in the answer
When will you NEVER need an absolute value bar in a radical?
when theres an odd index (such as 3)
6 (index=3)√5
six cube root of 5
what are extremas called that are either the lowest of the minimums or the highest of the maximums
absolute extrema (min/max)
What are all extremas called regardless of their size in relation to other extremas
relative extrema
what are factors called when its the same binomial with opposite signs?
(x+5)(x-5)
congugates
what does standard form mean? are there usually fractions
you are supposed to multiply out the factors and there usually arent fractions
the max number of zeroes in any function is directly based on the number of the ________
degree
the max number of relative zeros is the same number as the
degree - 1
true/false: every absolute extrema is a relative extrema
true
true/false: every relative extrema is an absolute extrema
false
Polynomial functions and their name by degree: 0
constant
Polynomial functions and their name by degree: 1
linear
Polynomial functions and their name by degree: 2
quadratic
Polynomial functions and their name by degree: 3
cubic
Polynomial functions and their name by degree: 4
quartic
Polynomial functions and their name by degree: 5
quintic
Polynomial functions and their name by degree: 6
6th degree polynomial
Polynomial functions and their name by degree: 99
99th degree polynomial
behavior of a graph as x approaches positive infinity and negative infinity
end behavior
where the graph crosses the x-axis
real zeroes
coefficient of the term with the highest degree
leading coefficient
for a polynomial of one variable, its the greatest exponent of its variable
degree
key on the calc that can be used when you’re trying to find when an equation has an exact x given.
F(5), F(1/2), F(0.999)
store
what does the word “polynomials” mean?
many terms
a comparison of things that aren’t equal
inequality
numbers that can be plotted on a number line (1/2, 5, -0.22222, square root of anything positive)
real
the positive integer whole numbers (1,55, square root of a perf square)
natural
a number that can be expressed as a fraction with a denominator other than zero (5, 1/6, -8/13)
rational
any number that can be counted as a whole with no parts (1, 2, 7, -33)
whole
cannot be expressed on a number line (square root of a negative)
imaginary
a set of positive/negative whole numbers excluding zero (-12, 15, 1, 2/1)
integer
numbers with a decimal that doesnt simplify, cannot be written as a fraction ( 0.123257483928347)
irrational
