equations needed for SAT math

slope

m=y2-y1/x2-x1

Slope-Intercept Form

y = mx + b

Point-Slope Form

y-y1=m(x-x1)

Standard Form

Ax+By=C

Midpoint Formula

(x1+x2/2, y1+y2/2)

Distance Formula

d=squareroot of (x2-x1)²+(y2-y1)²

vertex Form

y=a(x-h)²+k (vertex is (h,k))

Quadratic Formula

x= -b plus or minus the square root of b²-4ac all over 2

Vertex x-coordinate:

x= -b/2a

Difference of Squares

x²-y²=(x-y)(x+y)

Percent Change

new value - old value/old value x 100

Average (Arithmetic Mean):

sum of numbers/number of values

Distance, Rate, Time:

d=rt

SOHCAHTOA

sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent

Degrees to Radians

radians = degree x π/180

Imaginary Unit

i = square root of -1

i² = -1

i³ = -i

i^4= 1

sum of roots

x1+x2= -b/a

product of roots

(x1)(x2) = c/a

standard circle equation

(x-h)²+(y+k)²=r²

h & k are the center/vertex

r = radius

perfect squares

x²+2xy+y²=(x+y)² and x²-2xy+y²=(x-y)²

standard form of parabola:

y=ax²+bx+c

a tells us if opens up or down

c is the y-int

x is the coordinate of parabolas vertex -b/2a

exponential function

f(x)=a(b²) + c

a is the starting point

b is ratio of change

c is vertical shift

compound interest

A=P(1+r/n) ^nt

graph amplification rules

2f(x) = graph moves farther from x-axis

1/2f(x) = graph moves closer to x-axis

parallel and perpendicular lines

parallel lines = same slope

perpendicular lines = slopes are negative reciprocals

discriminant:

b²-4ac

> 0 = 2 answers

= 0 = 1 answer

< 0 = 0 answers

complementary angles

sin(x)=cos(90 degrees - x)

arc length from central angle

arc length/circumference=central angle/360

area of a sector

area of sector/circumference of circle = central angle/360