Pre Calculus Unit 5 Jeporady

Polynomial Rules

100

is this a polynomail

6x^4+3x^3+2x^2-x^-1

200

If the exponent at the specific zero, example: (x-3)^4, the graph will _______ the y axis at x=3.

bounce on

300

If the exponent at the specific zero, example: (x-3)^3, the graph will _______ the y axis at x=.

pass through

400

end behavior for this function: -3x(x+1)²(x-2)⁵(x-3)²

down, down

500

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

Functions of A,B,C, D

100

The A value only effects _-values, ____ing them if less than 1, and _____ing them if greater than 1

y, compressing, stretching

200

The D value only affects _-values, moving them _____ if positive and _____ if negative

y, up, down

300

The C value only affects _-VALUES, moving them _____ if positive and _____ if negative. 

x, right, left

400

The B value only effects _-values, _____ing them if less than 1 and ______ing them if greater than 1

x, stretch, compress

500

While doing horizontal transformations, you use _______ for vertical transformation order and you use _______ for horizontal. 

PEMDAS, SADMEP

List transformations

100

y=-x²

reflected

200

y=-2|x-2|

reflected, vertical stretch 2 (y-values), right 2

300

y=2|x|+4

vertical stretch 2, up 4

400

y=|2x-4|

factor: y=|2(x-2)|

horizontal compression 1/2, right 2

500

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

Find Zeros

100

(x-2)(x+1)

zeros: 2, -1

200

x²+10x+16

(x+8)(x+2)

Zeros: x-8, x-2

300

y=x³-625x

y=x(x²-625)

y=x(x+25)(x-25)

zeros: 0, -25, 25

400

y=x⁴-81x²

factor: x²(x²-81)

x²(x+9)(x-9)

zeros: 0,-9,9

500

y=x⁴-10x²+9

(x²-9)(x²-1)

(x+3)(x-3)(x+1)(x-1)

zeros: -3,3,-1,1

Sketch the graph

100

y=-2x

decreasing line

slope 2

200

y=x²-8x+12

vertex?

parabola

(4,-4)

300

(x+1)(x-3)²
include end behavior and pass/bounce on zeros

down, up

pass x=-1

bounce x=3

400

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

500

x⁴-625x²

^{end behavior}

^{pass/bounce at zeros}

up, up

x²(x²-625)

x²(x+25)(x-25)

x=0 pass, x=25 pass, x=-25 pass