cubic function

a polynomial function of degree 3

zero of a function

value of x that makes y = 0 same as x-intercept

double zero

cubic function w/ a squared factor

triple zero

a cubic function w/ a cubed factor

y = (x - 2)^{3}

y = (x - 2)^{2}(x + 1)

y = (x - 2)(x + 1)(x + 4)

steps to graph a cubic function on paper

1. draw the x-intercepts

2. make a table with x-values left of the x-intercepts, b/w each of them, and to the right of them

3. solve for y

steps to solve a cubic equation without graphing

1. put y on left side and set it to 0

2. find the GCF of the right side if possible and factor it out

3. if ax^{2} + bx + c format, use quadratic formula

how to solve cubic equations with calculator

1. input equation

2. find x-intercept (where y = 0)

square root of negative number

becomes i x pos. square root

parametric equation

equations where two variables are expressed in terms of a third variable.

parameter

3rd variable of a parametric equation

(parametrics) how to graph

1) make a table of values (time, x, y)

2) graph using x & y

how to write an equation for y in terms of x

1) solve for t with either of the equations (preferably x)

2) substitute into the other equation not used in step 1, t

3-dimensional coordinate plane

how to find a coordinate on a coordinate plane

3D midpoint formula

(x_{1} + x_{2}/2, y_{1} + y_{2}/2, z_{1} + z_{2}/2)

length of a diagonal of a rectangular prism

with edgesof length x, y, and z & a diagonal of length d

d = the square root of x^{2} + y^{2} + z^{2}

3D distance formula

d = square root of (x_{2 }- x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}