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point slope form

y - y1 = m(x - x1)

slope intercept form

y= mx+b

difference of cubes

x³ - y³ = (x - y)(x² + xy + y²)

sum of cubes

x³ + y³ = (x + y)(x² - xy + y²)

quadratic formula

x = -b ± √(b² - 4ac) / 2a

quadratic equation

ax² + bx + c = 0

standard form for equation of a circle

(x - m)² + (y - n)² = r² if (m,n) was your center point

difference of squares

x² - y² = (x + y)(x - y)

imaginary numbers

√(-1) = i

sum of squares

x² + y² = (x² + xy + y²)

distance formula

d = √( x2- x1) + (y2 - y1)

midpoint formula

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

a graph is symmetric with respect to the x-axis when (x,y)...

and (x, -y) is also on the graph

a graph is symmetric with respect to the y-axis when (x,y)...

and (-x,y) is also on the graph

a graph is symmetric with respect to the origin when (x,y)...

(-x, -y) is also on the graph

completing the square

x² + bx +( b / 2)² = (x + b / 2)²

principal square root of a number

√(-a) = √(ai)

slope of a line passing through two points

m = y2 - y1 / x2 - x1

a line is parallel if

slopes are equal EX: m1 = m2

line is perpendicular if

slopes are negative reciprocals EX: m1 = (-1 / m2)

a function is even if

f(-x) = f(x)

a function is odd if

f(-x) = -f(x)

greatest integer function is

slanted ladder

vertical shift upward is

h(x) = f(x) + c

vertical shift downward is

h(x) = f(x) - c

horizontal shift to the right

h(x) = f(x - c)

horizontal shift to the left

h(x) = f(x +c)

reflection in the x-axis

h(x) = -f(x)

relection in the y-axis

h(x) = f(-x)

sum of a function

(f + g)(x) = f(x) +g(x)

difference of a function

(f - g) (x) = f(x) - g(x)

product of a function

(fg)(x) = f(x)g(x)

quotient of a function

(f / g)(x) = f(x) / f(x)

compostion of a function

(f o g)(x) = f(g(x))