when you're given the slope of a line and one point, what formula do you use?
Point-Slope Form: y-y1=m(x-x1)
When you're given only two points , find the equation of the line by:
1.) first, finding m: y2-y1/x2-x1 2.) then, plug m in to the point-slope form equation and use either set of points.
if two lines are perpendicular, their slopes will be:
Reciprocal and opposite (if one is +, the other will be -)
to find a common intersection between three lines, you must:
1.) set two of them equal to each other and solve for x 2.) plug x and either m value into the equation to get y 3.) plug x and y back into the equation with no numerical values and solve for m
given g(x) = f(x+b) +c. where in this function can you find the shifts?
f= stretched or shrunk by this value (x+b) = shifted to the left or right by this value c= shifted up or down by this value - or + (f) = denotes the direction the parabola will open
how do you find the vertex from an equation in the form (x+t)2 + c
t(f(t)) is the vertex. or, (t,c)
how do you find the degree of a polynomial?
find the highest power in the polynomial; this is the degree
for |x| very large, the numerator and denominator (largest terms excluded):
are approximately 1
what is a rational function?
a function of the form r(x) = p(x) / q(x) where p and q are polynomials, and q can't equal 0.
How do you divide polynomials?
use standard long division
i2 = ?
define a sum and difference of two complex numbers
(a+bi) + (c+di) = (a+c) +(b+d)i
(a+bi)-(c+di) = (a-c) + (b-d) i
What is the complex conjugate?
if the expression is (a + bi), its complex conjugate is (a-bi)
Define multiplication of complex numbers
(a+bi)(c+di) = (ac-bd) + (ad-bc)i
Define division of complex numbers
(a+bi) / (c+di) = (ac + bd/c2+d2) + (bc-ad/c2+d2) i
What are the three ways to solve systems of linear equations?
substitution, standard elimination, and gaussian elimination with matrices
logby= x is the inverse of?
logb (x/y) =
Describe the expression B(t) = Pert
B(t) = final amount
P= initial amount
r = growth/decay rate
what is the equation for the distance between two points?
√( (x2-x1)2 +(y2-y1)2)
What is the equation for the midpoint of a line?
(x1+x2/2 ), (y1+y2/2)
What is the equation of a circle?
(x-h)2 +(y-k)2 = r2
Area of a trapezoid
Area of an ellipse/ equation in ellipse form
area = πab when the equation is in x2/a2+y2/b2=1 form
Area Stretch Theorem
The area of R' = cd times the original area (R)
what is the definition of e?
e is the number such that area(1/x,1,e) =1
lnx is a shorthand way of writing what?
What is the equation for the doubling time of a system?
70/R, where r = growth rate
What is the equation for the doubling rate of a system?
70/t, where t=time in years
how do you find the center, r, and area of a circle given in x2+hx+y2+ky=c form?
you complete the square, yielding the form (x-h)2+(y-k)2=r2. from here you can find the center (h,k) and radius (r). area = πr2
Cos(any ø)2 +sin(any ø)2 always equals...
any point in the region from π/2-->π is...
what is the equation to find arc length?
what is the equation to find the area of a slice?
How do you convert from degrees to radians?
how do you convert from radians to degrees?
how do you find the 4 smallest + numbers ø such that sin or cosø = 0,-1 or 1?
go around the unit circle counterclockwise, stopping each time sin or cos= given integer x. do this 4 times. find the 1st one, add 2π to it to get the next one, etc...
how do you find the 4 smallest + numbers ø such that sin or cosø = 1/2 or √3/2?
find the first ø. (ex 30º). find the next ø in line on the unit circle (ex 150º). these are your 1st two numbers. Then, add your original ø to 360º, which yields the 3rd number. finally, add your second ø to 360 to get the 4th number.
what is another way to write cotangent?
write tanø in terms of cosø
write secant in terms of tanø
what are the 3 trig identities with (π/2-ø)?
cos(π/2-ø) = sinø
sin(π/2-ø) = cosø
tan(π/2-ø) = 1/tanø
What are the 3 trig identities with (90-ø)?
What are the 3 trig identities with (ø+π)?
cos(ø+π) = -cosø
sin(ø+π) = -sinø
tan(ø+π) = tan ø
what are the 3 trig identities with (ø+2π)?
cos(ø+2π) = cosø
sin(ø+2π) = sinø
tan(ø+2π) = tanø
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