Algebra II TRIG Flashcards

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# Algebra II TRIG Flashcards - PowerPoint PPT Presentation

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

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?
• 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)

What is it good for?

#1

What is it good for?

#2

Tells us the roots

(x-intercepts).

#2

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

#3

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 = kxCharacteristics: y –int = 0 (always!)Sketch: (any linear passing through the origin)

#4

Define Inverse Variation

#5

Give a real life example

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.

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

#6

xy = k or .

HYPERBOLA (ROTATED)

#6

### FUNCTIONS

BLUE CARD

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
• Each member of the DOMAIN is paired with one and only one member of the RANGE.

#9

### 1-to-1 Function: A function whose inverse is also a function.

Horizontal Line Test

#10

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

#11

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

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

1.) Notation:

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

3.) …then point (b,a) lies on

#12

SHIFTSLet f(x) = x2

Describe the shift performed to f(x)

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

#13

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

YELLOW CARD

### Describe How to Graph Complex Numbers

#15

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?

|a + bi|

|2 – 5i|

#16

Pythagorean Theorem

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16

POSITIVE,

PERFECT SQUARE?

#18

ROOTS = Real, Rational, Unequal
• Graph crosses the x-axis twice.

#18

POSITIVE,

NON-PERFECT SQUARE

#19

ROOTS = Real, Irrational, Unequal
• Graph still crosses x-axis twice

#19

ZERO

#20

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

#20

ROOTS = IMAGINARY
• GRAPH NEVER CROSSES THE

X-AXIS.

#21

SUM =
• PRODUCT =

#22

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

#23

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

#24

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

3 – 4i

#25

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

#26

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

#27

• Square both sides
• Solve
• CHECK!!!!!!!!!

#28

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

#29

• Find a common denominator
• Simplify
• KEEP THE DENOMINATOR!!!!!!

#30

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

#31

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

conjugate 4 – 3i

#33

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

#35

• The numbers under the radical must be the same.

#36

When you multiply…

the base and

the exponents

#37

KEEP (the base)