(a_n) = (a0) * ( (r)^(n-1) )
a_n == The target number based on n
a0 == the zeroth number in the set
r == the rate of change per increment of n
-1 == an offset to help start the sequence at the appropriate spot
July 31, 2018
July 29, 2018
Notes on Parabolas
gravaljar seeks parabolic data
In a parabolic Quadratic Equation...
Standard Form: f(x) style.... the last number (constant) that has no variable next to it...should the Y-intercept.
VERTEX FORM: f(x):: The last constant is the vertex's y coordinate...
The x coordinate of the vertex is the opposite of the number to the right of "x" inside the parenthesis expression that is being squared.
EG: f(x) = -(x-2)^2 + 64 =====> VERTEX: (2, 64)
ANATOMY OF VERTEX FORM::
y = w*(x + k)^2 + h
w = If "w" is negative... the parabola faces down...
also, as "w" approaches zero, it gets wider and wider, making a more "shallow" parabola.
the larger the "w" number, the thinner the parabola gets. This is related to "stretching" the parabola.
k= the Horizontal offset for the parabola....
if "k" is negative, the parabola will be shifted to the right.
if "k" is positive, the parabola will be shifted to the left.
h = The vertical offset for the parabola.
If h is positive, the parabola will be shifted UP.
If h is negative, the parabola will be shifted DOWN.
COMPLETING THE SQUARE:::
STANDARD FORM:: ax^2 + bx + c = 0
VERTEX FORM:: a(x+d)^2 + e = 0
FIND "d" ==> d = (b) / 2a
FIND "e" ====> e = (c) - ( (b^2) / 4a)
-Tyler