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Algebra II TRIG Flashcards. As the year goes on we will add more and more flashcards to our collection. Bring your cards every TUESDAY for eliminator practice!

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algebra ii trig flashcards

Algebra II TRIG Flashcards

As the year goes on we will add more and more flashcards to our collection.

Bring your cards every TUESDAY for eliminator practice!

Your flashcards will be collected on every test day! At the end of the quarter the grade received will be equivalent in value to a test grade. Essentially, if you lose your flashcards it will be impossible to pass the quarter.

what will my flashcards be graded on
What will my flashcards be graded on?
  • Completeness – Is every card filled out front and back completely?
  • Accuracy – This goes without saying. Any inaccuracies will be severely penalized.
  • Neatness – If your cards are battered and hard to read you will get very little out of them.
  • Order - Is your card #37 the same as my card #37?
vertex formula axis of symmetry

Vertex Formula(Axis of Symmetry)

What is it good for?

#1

quadratic formula

Quadratic Formula

What is it good for?

#2

tells us the roots x intercepts
Tells us the roots

(x-intercepts).

#2

describe the steps for completing the square
Describe the Steps for “Completing the Square”
  • How does it compare to the quadratic formula?

#3

slide9

1.) Leading Coeff = 1 (Divide if necessary)2.) Move ‘c’ over3.) Half ‘b’ and square (add to both sides)4.) Factor and Simplify left side.5.) Square root both sides (don’t forget +/-)6.) Solve for x.*Same answer as Quadratic Formula.

#3

general form y kx characteristics y int 0 always sketch any linear passing through the origin
General Form: y = kxCharacteristics: y –int = 0 (always!)Sketch: (any linear passing through the origin)

#4

define inverse variation
Define Inverse Variation

#5

Give a real life example

slide13
The PRODUCT of two variables will always be the same (constant).

xy=c

  • Example:
    • The speed, s, you drive and the time, t, it takes for you to get to Rochester.

#5

state the general form of an inverse variation equation
State the General Form of an inverse variation equation.

Draw an example of a typical inverse variation and name the graph.

#6

xy k or
xy = k or .

HYPERBOLA (ROTATED)

#6

functions

FUNCTIONS

BLUE CARD

slide20
DOMAIN - List of all possible x-values

(aka – List of what x is allowed to be).

  • RANGE – List of all possible y-values.

#8

vertical line test
Vertical Line Test
  • Each member of the DOMAIN is paired with one and only one member of the RANGE.

#9

how do you find an inverse function algebraically graphically

How do you find an INVERSE Function… ALGEBRAICALLY?GRAPHICALLY?

#11

slide26
Algebraically:Switch x and y… …solve for y.Graphically:Reflect over the line y=x (look at your table and switch x & y values)

#11

slide27

1.)What notation do we use for Inverse?2.) Functions f and g are inverses of each other if _______ and ________!3.) If point (a,b) lies on f(x)…

#12

slide28

1.) Notation:

2.) f(g(x)) = x and g(f(x)) = x

3.) …then point (b,a) lies on

#12

shifts let f x x 2
SHIFTSLet f(x) = x2

Describe the shift performed to f(x)

  • f(x) + a
  • f(x) – a
  • f(x+a)
  • f(x-a)

#13

slide30
f(x) + a = shift ‘a’ units upward
  • f(x) – a = shift ‘a’ units down.
  • f(x+a) = shift ‘a’ units to the left.
  • f(x-a) = shift ‘a’ units to the right.

#13

complex numbers

COMPLEX NUMBERS

YELLOW CARD

slide35
x-axis represents real numbers
  • y-axis represents imaginary numbers
  • Plot point and draw vector from origin.

#15

how do you evaluate the absolute value magnitude of a complex number
How do you evaluate the ABSOLUTE VALUE (Magnitude) of a complex number?

|a + bi|

|2 – 5i|

#16

pythagorean theorem
Pythagorean Theorem

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16

slide40

POSITIVE,

PERFECT SQUARE?

#18

roots real rational unequal
ROOTS = Real, Rational, Unequal
  • Graph crosses the x-axis twice.

#18

slide42
POSITIVE,

NON-PERFECT SQUARE

#19

roots real irrational unequal
ROOTS = Real, Irrational, Unequal
  • Graph still crosses x-axis twice

#19

slide44
ZERO

#20

roots real rational equal
ROOTS = Real, Rational, Equal
  • GRAPH IS TANGENT TO THE X-AXIS.

#20

roots imaginary
ROOTS = IMAGINARY
  • GRAPH NEVER CROSSES THE

X-AXIS.

#21

slide49
SUM =
  • PRODUCT =

#22

slide51
Find the SUM of the roots
  • Find the PRODUCT of the roots

#23

slide53
One over what ever is given.
  • Don’t forget to RATIONALIZE
  • Ex. Multiplicative inverse of 3 + i

#24

slide55
What you add to, to get 0.
  • Additive inverse of -3 + 4i is

3 – 4i

#25

slide58
Split into 2 branches
  • Only negate what is inside the absolute value on negative branch.
  • CHECK!!!!!

#26

slide60
Factor and find the roots like normal
  • Make sign chart
  • Graph solution on a number line (shade where +)

#27

slide62
Isolate the radical
  • Square both sides
  • Solve
  • CHECK!!!!!!!!!

#28

slide65
Change Division to Multiplication flip the second fraction
  • Factor
  • Cancel (one on top with one on the bottom)

#29

slide67
FIRST change subtraction to addition
  • Find a common denominator
  • Simplify
  • KEEP THE DENOMINATOR!!!!!!

#30

slide69
First find the common denominator
  • Multiply every term by the common denominator
  • “KILL THE FRACTION”
  • Solve
  • Check your answers

#31

slide74
Change only the sign of the second term
  • Ex. 4 + 3i

conjugate 4 – 3i

#33

slide78
Multiply/divide the numbers outside the radical together
  • Multiply/divide the numbers in side the radical together

#35

slide80
Only add and subtract “LIKE RADICALS”
  • The numbers under the radical must be the same.
  • ADD/SUBTRACT the numbers outside the radical. Keep the radical

#36

slide82
When you multiply…

the base and

the exponents

#37

slide83
KEEP (the base)
  • ADD (the exponents)

#37

slide85
Keep (the base)
  • SUBTRACT (the exponents)

#38