Polynomial Operations
(x5 - 3x2 + 15) + (5x5 + 10x2 - 5)
6x5 + 7x2 + 10
Factor: x4 - 5x2 - 6
(x2 + 1)(x2 - 6)
Solve: x4 - 81 =0
x = 3, -3, 3i, -3i
What button do you click to type an equation?
"y =" (First grey button)
(x3 - 5x + 3) - (3x2 + 10x - 7)
x3 - 3x2 - 15x + 10
Factor: x3 + 27
(x + 3)(x2 - 3x + 9)
Solve: 2x3 - 5x2 + 8x - 20 = 0
x = 2, -2, 5/2
If a function with a degree of 7 has 3 real zeros, how many imaginary zeros does it have?
4 imaginary zeros
What button do I click to adjust how much of the graph I can see?
"Window" (2nd grey button)
20x8 - 26x7
Factor: 10x5 - 2x4 + 15x - 3
(2x4 + 3)(5x-1)
Solve (QF!): x2 - 7x = -5
x = (7 ± √ 29)/2
True or False: The range of an EVEN degree function is (-∞, ∞)
FALSE!
What do I do if I am given an x-value and need to find the y-value?
2nd → Trace → #1: Value (enter x=#)
(2x3 - 12)2
4x6 - 48x3 + 144
Factor Completely: 81x4 - 125
(9x2 + 25)(3x + 5)(3x - 5)
Solve (QF!): 2x2 - 11 = -6x
x = (-3 ± i√ 13)/2
What does a bounce on the x-axis represent?
2 solutions/zeros of the same value!
What do I do if I need to find the smallest x-intercept?
2nd → Trace → #2: Zeros → Find left-most x-int
(x2 - 9) ÷ (x + 5)
x - 5 + (16 ÷ (x+5))
Factor: -216x4 + 512x
-x(6x - 8)(36x2 + 48x + 64)
Solve: (x3 + 6x2 + 11x + 6) ÷ (x+3)
x = -3, -2, -1
For an NEGATIVE function, as x → ∞, y → ???
y → -∞
What do I do if I'm given a y-value and need to find the x-value?
Graph y=# → 2nd → Trace → #5: Intersect → Find intersection of 2 functions.