quadratic formula
compound interest formula
simple interest formula
distance formula
D=R X T
complex numbers
discriminant formula
if D> 0: 2 real solutions
if D<0: 2 non-real solutions
if D=0 : exactly 1 solution
factor by grouping
inequality signs
when the inequality sign changes
if you multiply or dividing both sides of the inequality by a negative number it changes the direction of the sign
when the inequality sign does not change
if you add or subtract both sides of the inequality
solving a compound inequality with and
it will involve the word and- first solve each inequality separately- then find the intersection of the two solution sets
interval notation of compound inequalities with the word or
will have the union sign U
greater/ less than or equal to
filled in circle
greater than/ less than
open circle
quadrants
midpoint formula
distance formula
standard form of a circle
center of the circle: (h,k)
radius: r
general form of a circle
converting general form to standard form
find the center, radius, and intercepts, rearrange the terms then complete the square then factor
positive slope
negative slope
zero slope
slope
m= rise/ run
point slope form
m: slope of the line
slope intercept form
m: slope
b: y intercept
standard form slope and y intercept
Ax + By = C slope: m= -A/B
y intercept: C/B
horizontal line equation
y = b b: the y coordinate of any point on the line
two non-vertical lines are parallel if
they have the same slopes
two non-vertical lines are perpendicular if
the product of their slopes is -1
vertical line test
when saying if a function is increasing, decreasing, or constant in interval notation use
parentheses and not brackets
even function
symmetric across the y axis
odd function
symmetric across the origin
constant function
identity function
square function: f(x)= x^2
cube function: f(x)= x^3
absolute value function: f(x)= lxl
square root function: f(x)= sqrtx
cube root function: f(x)= 3sqrtx
reciprocal function: f(x)= 1/x
greatest integer function
y= -f(x)
reflection about the x-axis
y= f(-x)
reflection about the y-axis
vertical stretch y= af(x)
multiply each y coordinate by a
horizontal compression
a>1: divide each x coordinate of y= f(x) by a
horizontal stretch
0<a<1: divide each x coordinate of y= f(x) by a
one-to-one function
a function is one-to-one if for any values a cant = b in the domain- can determine this using the horizontal line test
finding the inverse of a function
quadratic function
the porabola opens up if
the leading coefficient a>0
the porabola opens down if
the leading coefficient a<0
the standard form of a quadratic function
the vertex of a porabola: (h,k)
e
natural base
vertex formula
revenue equation
Revenue= Price x Quantity
R=PXQ
the right hand end behavior finishes up if
a>0
the right hand end behavior finishes down if
a<0
even degree end behavior
if the degree n is even the graph has the same left and right hand end behavior- it starts and finishes in the same direction
long division
synthetic division
can only be used if divided by form (x-c)
complex conjugate pairs theorem
when do vertical asymptotes occur
when the graph of a function approaches positive or negative infinity as x approaches some finite number a- cancel any common factors before locating the vertical asymptotes
if the degree of the denominator is greater than the degree of the numerator:
m>n
then y=0 is the horizontal asymptote
if m<n
then there are no horizontal asymptotes
if the degree of the denominator is equal to the degree of the numerator:
m=n
then the horizontal asymptote is y= an/bm
direct variation formula
y=kx
k: the constant of variation
inverse variation
joint variation formula
y=kxz
continuous compound interest formula
A: total amount after t years
P: original investment
r: interest rate per year
n: number of times interest is compounded per a year
t: number of years
method of relating the bases
if b^u= b^v then u=v