Math 126 Memorization List 1

Slope (m) formula

m = (y2 - y1) / (x2 - x1)

slope intercept form

y = mx + b

point-slope equation of a line

y - y1 = m(x - x1)

midpoint formula

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

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

average(mean)

sum of terms / number of terms

median

number in the middle

mode

number that occurs the most

average speed (velocity)

total distance/total time

perimeter of a rectangle

P= 2l + 2w

area of a triangle

A = 1/2bh

(b = base, h = height)

Pythagorean Theorem

a²+b²=c²

area of a trapezoid

A=1/2h(b1+b2)

area of a circle

A=πr²

circumference of a circle

C=2πr

surface area of a sphere

SA=4πr²

volume of a rectangular solid

V=lwh

(length width height)

Volume of a sphere

V=4/3πr³

Domain

Set of all possible x-values for a function

Range

Set of all possible y-values for a function.

quadratic formula

x = -b ± √(b² - 4ac)/2a

shift down c units

y = f(x) - c

shift up c units

y = f(x) + c

shift left c units

y = f(x+c)

shift right c units

y=f(x-c)

reflect over x-axis

y = -f(x)

reflect over y-axis

y = f(-x)

vertical stretch by factor a

y = a * f(x)

horizontal stretch by factor a

y = f(ax)

ln e

1

ln 1

0

logb x = y

b^y = x

expand logb xy

logb x + logb y

expand logb x/y

logb x - logb y

expand logb x^n

n * logb x

change of base

logb x = log x / log b