Section 1
Preview this deck
Conjugate
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
4 years ago
Date created
Mar 1, 2020
Cards (142)
Section 1
(50 cards)
Conjugate
Used to rationalize the denominator of a fraction.
Properties of Quadratics in Standard Form
-The vertex is (-b/2a , f(-b/2a)) -The axis of symmetry is x=-b/2a -The y-intercept is C -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent
Rate of Change
Slope that represents how much one quantity changes on average, relative to the change in another quantity.
GCF
Greatest Common Factor
Properties of 'i'
-'i'='i' -'i^2'=-1 -'i^3'='-i' -'i^4'=1 -'i^5'='i' -'i^6'=-1 -'i^15'=-1 -'i^34'=-1
Function
A relation for which each input has exactly one output.
Vertical Line Test
A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.
Expression
A finite combination of symbols that are well-formed according to applicable rules.
Properties of Quadratics in Vertex Form
-The vertex is (h,k) -The axis of symmetry is x=h -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent
Parallel Lines
Lines are parallel if and only if they have the same slope.
>
Greater Than
Elimination
Range
Set of all output values.
Simple Interest Formula
I=Prt -P=principal (original amount of money) -r=interest rate (written as a decimal) -t=time (years)
Parent Function
The most basic function in a family.
General Equation of an Absolute Value Function
y=a|x-h|+k -a=rate of change -(h,k)=vertex
Difference of Squares
Relation
A mapping, or pairing, of input values with output values.
Domain
Set of all input values.
Vertex Form of Quadratic Functions
y=a(x-h)^2 +k -a≠0 -the graph is a parabola -Parent Function is f(x)=x^2
Slope
Denoted by 'm,' of a non-vertical line is the ratio of the vertical change to the horizontal change.
Point-Slope Form
y − y1 = m(x − x1). -m=slope -(x1,y1)=a given point
Piecewise Functions
A function that is defined by more than one function.
Pythagorean Theorem of Baseball
W/T≈R^2/R^2+A^2 -W=wins -T=games played -R=runs scored -A=runs allowed
Celcius to Fahrenheit Conversion Formula
F=(9/5)C+32 -F=degrees (fahrenheit) -C=degrees (celsius)
<
Less Than
Absolute Value Graphs
Parabola
Standard Form of Linear Equations
A linear equation in the form 'Ax+By=C.'
Constant
A non-varying value.
Zeroes
Solutions (also see 'Root / X-Intercept / Zero')
Slope-Intercept Form
y=mx+b -m=slope -b=y-intercept
Absolute Value
The distance a number is from 0 on a number line. (Can never be negative.)
Alternating Current Voltage Formula
E=IZ
Square Root
A number, 'r,' is a square root of a number, 's,' if r^2=s. -3^2=9 and (-3)^2=9 so 3 and -3 are square roots of 9
Function Notation
y=f(x), the value of the function when x is a certain value.
Imaginary Numbers
A complex number that can be written as a real number multiplied by the imaginary unit 'i.'
G.E.M.D.A.S
Grouping, Exponents, Multiplication, Division, Addition, Subtraction
LCM
Least Common Multiple
Radical
Operator to the square root.
Substitution
Coefficient
A multiplicative factor in some term of a polynomial, a series, or any expression.
Principal Square Root
The positive square root.
Variable
A symbol that represents a quantity in a mathematical expression, as used in many sciences.
Standard Form of Quadratic Functions
y=ax^2 +bx+c -a≠0
Term
A component of a logical or mathematical expression.
Zero Product Property
If AB=0, then A=0 or B=0.
Complex Numbers
A number that can be expressed in the form 'a+bi,' where 'a' and 'b' are real numbers and 'i' is the imaginary unit, that satisfies the equation i^2=-1.
Perpendicular Lines
Lines are perpendicular if and only if they have negative reciprocal slopes.
Radicand
Expression under the radical.
Section 2
(50 cards)
Properties of Logarithms
-log(b) xy = log(b) x + log(b) y -log(b) x/y = log(b) x - log(b) y -log(b) x^y = ylog(b) x
Radical Form to Rational Exponent Conversion
ā81=81^¼ Even Roots: -a < 0: no real nth roots -a = 0: one real nth root (0) -a > 0: two real nth roots Odd Roots: one real nth root
Completing the Square
Change-Of-Base Formula
log(c) a = (log a) / (log c)
Percent Decrease Model
y=a(1 - r)^t -a=initial value -r=% increase (or decrease) -t=time
End Behavior
The behavior of the graph of f(x) as 'x' approaches positive infinity or negative infinity.
Factoring by Grouping
The process of factoring four terms by grouping them in pairs, factoring the GCF from each pair, and looking for a common binomial factor.
Quadratic Formula
Common Logarithm
log(10) x written as log x
Power Function
y=ax^b, where 'a' is a real number and b is a rational number.
Inverse Relation
An interchange of the input and output values of the original relation.
Vertical Motion Quadratic Function
h(t)=-16t^2+vt+s -h=height of object (feet) -t=time (seconds) -v=initial velocity of object (ft/sec) -s=initial height of object (feet)
Exponential Growth Function
An exponential function that 'grows' away from the asymptote as you move left to right. -b > 1
Square Root Function
f(x) = √x
Rational Exponent Rules
-a^m * a^n = a^m+n -(a^m)^n = a^mn -(ab)^m = a^m * b^m -a^-m = 1/a^m -a^m / a^n = a^m-n. -(a/b)^m = a^m / b^m -ax^m ± bx^m = (a ± b)x^m
Extrema
The collection of the largest and smallest values of a function.
Asymptote
An imaginary line that a graph approaches more and more closely.
Periodic Compounding Interest Formula
A=P(1+r/n)^nt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal) -n=number of times the interest is compounded (paid) per year
f(x)=(√x) +k
Translates square root function 'k' units vertically.
Decibel Level Formula
D(I) = 10log(I/10^-12) -D(I)=the decibel level as a function of I -I=intensity of the sound (watts per square meter) -10^-12=intensity of the quitest sound a human can hear
Polynomial Graphs
Product Property of Radicals
√ab = √a * √b
Polynomial Function
f(x)=ax^n +bx^n-1 +cx^n-2+...+dx+e -a=leading coefficient -n=degree
e
The base of the natural logarithm. Approximately equal to 2.718281828459, it is the figurative asymptote of the function (1+1/n)^n.
Horizontal Line Test
The inverse of a function 'f' is also a function if and only if no horizontal line intersects the graph of 'f' more than once.
Quotient Property of Radicals
√(a/b) = (√a) / (√b)
Discriminant
A function of a polynomial's coefficients, giving information about the nature of its roots. -If b^2-4ac > 0, the (2) roots are positive -If b^2-4ac < 0, the roots are negative and imaginary -If b^2-4ac = 0, the (1) root equals zero
Factoring with Cube Patterns
Absolute (Global) Extrema
The collection of the largest and smallest values on the entire domain of a function.
Exponential Decay Function
An exponential function that 'decays' towards the asymptote as you move left to right. -0 < b < 1
Exponential Function
y=a(b)^x, a function in which the variable is in the exponent. -a=initial value -b=growth/decay factor
Logarithm
The inverse operation to exponentiation. y = log(b) x if and only if b^y = x -b > 0 -b ≠ 1 -x > 0
Root / X-Intercept / Zero
Where a function crosses the x-axis.
Composition of a Function
h(x)=g(f(x)), the pointwise application of one function to the result of another to produce a third function.
Continous Combounding Interest Formula
A=Pe^rt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal)
Annual Price of Gasoline Cubic Function
c(t)=0.0007t^3 - 0.014t^2 + 0.08t + 0.96
Factoring Polynomials in Quadratic Form
It is sometimes necessary to factor out any factor that might be common to all terms first. The two terms in 5x^2 - 10, for example, both contain the factor '5'. This means that the expression can be rewritten as 5(x^2 - 2).
Cubic Root Function
f(x) = a(ā(x-h)) + k a: -if |a|gets bigger, then there is a vertical stretch -if |a| gets smaller, then there is a vertical shrink -if a is negative, then the graph flips h: -translates graph 'h' units horizontally k: -translates graph 'k' units vertically
Two-Step Factoring
First, factor out any GCF from the original problem, then factor normally.
Simplest Form of Radicals
No perfect nth powers as factors and any denominator has been rationalized.
Synthetic Substitution
Relative (Local) Extrema
The collection of the largest and smallest values of a function within a given range.
Synthetic Division
Exponent Rules
-a^m * a^n = a^m+n -a^m / a^n = a^m-n. (a≠0) -(a^m)^n = a^mn -(ab)^n = a^n * b^n -(a/b)^n = a^n / b^n -a^-n = 1/a^n -a^0 = 1. (a≠0)
Polynomial Long Division
Percent Increase Model
y=a(1 + r)^t -a=initial value -r=% increase (or decrease) -t=time
Inverse Function
When both the original relation and the inverse relation are functions. -Written as f^-1(x) ā© NOT A NEGATIVE EXPONENT!
f(x)=√(x-h)
Translates square root function 'h' units horizontally.
Logarithmic Functions
Natural Logarithm
log(e) x written as ln x
Section 3
(42 cards)