Factor Completely
Solve
Don't Cross Me
Sketch That Graph
Final Jeopardy
100
x4 - x2 - 72
(x2 + 8)(x - 3)(x + 3)
100
x4 = 12x2 - 32
x = (2√2, 2, -2)
100
f(x)=x4 - 4x2 + 3
X-intercepts ( √3, -√3, 1, -1)
100
For f(x)=4x4 - 37x2 + 9
What is the end behavior and Y-intercept
As x approaches ∞ y approaches ∞
As x approaches -∞ y approaches ∞
y intercept (0, 9)
200
x6 - 6x5 - x4 + 6x3
x3(x - 6) (x + 1) (x - 1)
200
x3 - 3x2 = –2x
x = (2, 1, 0)
200
f(x)=3x3-7x2+27x-63
X-intercept: (7/3, 0)
200
For f(x)=–2x4 + 10x3 + 28x2
What is the end behavior and Y-intercept
As x approaches ∞ y approaches -∞
As x approaches -∞ y approaches -∞
y intercept (0, 0)
300
125x3+27
(5x + 3)(25x2 - 15x + 9)
300
x3 = 64
x = 4, x =-2 - 2i√3, x =-2 + 2i√3
300
f(x)=–15x3-5x2+50x
X-intercepts ( 0, 5/3, -2)
300
For f(x)= x3 + 5x2 - 25x - 125
Zeros, multiplicity, cross/bounce:
Zero Multiplicity Cross/Bounce
5 1 Cross
-5 2 Bounce
400
8x3 - 1
(2x -1)(4x2 +2x + 1)
400
x3 + 2x2 = 9x + 18
x = (3, -2, -3)
400
f(x)=27x3+8
X-intercept: (-2/3, 0)
400
For f(x)= –x3 - 3x2 + 40x
Zeros, multiplicity, cross/bounce:
Zero Multiplicity Cross/Bounce
0 1 Cross
-8 1 Cross
5 1 Cross
500
10x3 + 22x2 - 24x
2x(5x -4)(x + 3)
500
4x4 + 21 = –31x2
x= ( -i√7, i√7, (-i√3)/2, (i√3)/2 )
500
DAILY DOUBLE
How many vowels are in my last name?
3: K e h o e
500
For f(x)= 4x4 - 37x2 + 9
Sketch
y intercept:(0, 9)
x intercepts: (-1/2, 0), (1/2, 0), (3, 0), (-3, 0)
500
f(x) = (-x3 + x2)/2 + x