Polynomial Rules
6x^4+3x^3+2x^2-x^-1
The A value only effects _-values, ____ing them if less than 1, and _____ing them if greater than 1
y, compressing, stretching
y=-x2
reflected
(x-2)(x+1)
zeros: 2, -1
y=-2x
decreasing line
slope 2
If the exponent at the specific zero, example: (x-3)^4, the graph will _______ the y axis at x=3.
bounce on
The D value only affects _-values, moving them _____ if positive and _____ if negative
y, up, down
y=-2|x-2|
reflected, vertical stretch 2 (y-values), right 2
x2+10x+16
(x+8)(x+2)
Zeros: x-8, x-2
y=x2-8x+12
vertex?
parabola
(4,-4)
If the exponent at the specific zero, example: (x-3)^3, the graph will _______ the y axis at x=.
pass through
The C value only affects _-VALUES, moving them _____ if positive and _____ if negative.
x, right, left
y=2|x|+4
vertical stretch 2, up 4
y=x3-625x
y=x(x2-625)
y=x(x+25)(x-25)
zeros: 0, -25, 25
down, up
pass x=-1
bounce x=3
end behavior for this function: -3x(x+1)2(x-2)5(x-3)2
down, down
The B value only effects _-values, _____ing them if less than 1 and ______ing them if greater than 1
x, stretch, compress
y=|2x-4|
factor: y=|2(x-2)|
horizontal compression 1/2, right 2
y=x4-81x2
factor: x2(x2-81)
x2(x+9)(x-9)
zeros: 0,-9,9
y=-x3+16x
end behavior
pass/bounce on zeros
up,down
y=-x(x2-16)
y=-x(x+4)(x-4)
x=0 pass, x=4 pass, x=-4 pass
Write in standard form AND list end behavior.
y=4x(x+1)(x-1)(x-9)2
y=4x5-72x4+472x3+72x2-324x
end behavior: down, up
While doing horizontal transformations, you use _______ for vertical transformation order and you use _______ for horizontal.
PEMDAS, SADMEP
y=-4|6x-12|+2
factor: y=-4|6(x-2)|+2
vertical reflection, vertical stretch 4, horizontal compression 1/6, right 2, up 2
y=x4-10x2+9
(x2-9)(x2-1)
(x+3)(x-3)(x+1)(x-1)
zeros: -3,3,-1,1
x4-625x2
end behavior
pass/bounce at zeros
x2(x+25)(x-25)
x=0 pass, x=25 pass, x=-25 pass