9.4-9.6 Flashcards
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
- draw the x-intercepts
- make a table with x-values left of the x-intercepts, b/w each of them, and to the right of them
- solve for y
steps to solve a cubic equation without graphing
- put y on left side and set it to 0
- find the GCF of the right side if possible and factor it out
- if ax2 + bx + c format, use quadratic formula
how to solve cubic equations with calculator
- input equation
- 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
(x1 + x2/2, y1 + y2/2, z1 + z2/2)
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 x2 + y2 + z2
3D distance formula
d = square root of (x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2
