3D space
3 dimensions or axies (x,y,z)
one value in 3d spaces (ex: y=5)
a plane
hint towards the dimension
3 variables = 3D
What a missing variable means in 3D (ex: x squared + z squared=1)
the equation’s shape will go along that axis
what a seperate variable means (ex: x squared + y squared = 1, z=5)
the equations shape will be about that separate variable’s position
sphere equation
x squared + y squared + z squared = r squared
how to shift a circle
(x-a)squared + (y-b) ^2 = r^2
how to shift a sphere
(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2
how to prove an equation is of a sphere
complete the square
completing the square equation
ax^2 +bx +(b/2a)^2- (b/2a)^2
Symbolism of Distance Formula
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2D distance formula
square root of (x1-x2)^2 + (y1-y2)^2
3D distance formula
square root of (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2