Math Flashcards
What is a parrallogram
Opposite sides are parrallel, IDENTICAL SLOPES
what is a rhombus
opposite sides are parrallel, and all sides are the same legnth
What is a rectangle
Opposite sides are parrallel, and adjacent sides are perpendicular
Square
Opposite sides are parrallel, all sides are the same legnth, adjacent sides are perpendicular
Is it in, out or on the circle
Calculate legnth,
if less = in
if more = out
if equal = on
What is the perpendicular bisector of a cirlce
Runs through the midpoint of the the chord, and goes through the circle
Radius
(x-h)^2+(y-k)^2=r^2
Trapezoid
1 pair of opposite side are parallel, parrallel sides are NOT the same legnth
Solving graphically
potting both lines to find the POI
solving by substitution
isolate one variable in one of the equations, substiture this value into the other equation and solve for remaining variable. Sub this value into either equation to get 2nd variable
solvign by elemination
multiply one or both equations such that the coefficients on one of the two variables are the same in both equations. Add/subtract the two equations to eliminate this variable. SUb this value into either equation to get the 2nd variable
slope formula
Y2-Y1/X2-X1
standard form
Ax+By=C
slope intercept form
y=mx+b
Midpoint formula
(x2+x1/2), (y2+y1 /2)
if two legnths are parallel their slopes are
the same
if two lines are perpendicular their slopes are
negative reciprocal
equilateral
3 sides are the same side
scalene
all sides are different legnths
isosceles
2 different angles
altitude
e is the perpendicular drawn from the vertex of the triangle to the opposite side.
right (perpendicular) bisector
midpoint of opposite side, perpendicular
median
midpoint to opp vertex
legnth
l= √((x_2-x_1)²+(y_2-y_1)²)
sine
opp/hyp
cos
adj/hyp
tan
opp/adj
how to solve for angle
x^-1
sine law
side/sin = side/sin =side/sin
cosine law solving for side
a2= b2 + c2 - (2bc cos a
cosine law solving for angle
cos (A) = (b2+c2 - a2) / 2bc
finding shortest distance
equation of the line, perpendicular of that, equation of perp, then legnth
what is the axis of symmetry
divides the parabola in half
y-value of the vertex is called
optimal value
standard form parabola
y=ax2+bx+c
factored form quadratic
y=a(x-r)(x-s)
vertex form
y=a(x-h)2+k
maximum vs minimum
-a value, positive a value
what is a root
x intercept
when you can’t solve by factoring you use
quadratic formula
quadratic formula
x= (-b + or - square root b2-4ac)/ 2a
what is the discriminant
b2-4ac
under the discriminant positive how many roots?
2
under the discriminant negative how many roots?
0
under the discriminant is 0 how many roots?
1
what is the base parabola
y=x^2
higher a value means, lower a value mean
thinner, thicker
a=+, a=-
+ opens up, - opens down
k value
out of the brackets, if k is greater than 0 moves up, bigger than 0 opens down.
Vertex is 0,k
h value
inside brackets,
if h is greater than zero graph goes right (x-h) ->
if h is less than zero graph goes left (x+h) <-
vertex is h,k
axis of symetry is x=h
reflected y-int
the other x value that will give you that y value of the y int
finite differences
differences between the first differences, i
angle of elevation
horizontal is on bottom, looking up from corner
angle of depression
horizontal on top, looking down
POI of the three perp bisectors is called
circumcenter, if you were to draw a circle from point would hit all vertexes
POI of three altitudes
orthocenter
POI of three medians
centroid
difference of squares
(a+b)(a-b)
perfect square
(a+x)^2 = a^2 + ax +x^2
(a-x)^2 = a^2 - ax +x^2
