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Unit #6 Radicals and Complex Numbers and Unit #7 Transformations
Reflective Portfolio
Section #1: Vocabulary
Define each:
 Redraw and label with the correct word (index, radicand, exponent, radical)
aa
xxbb

Imaginary Number:

Complex Number:

Conjugate:

Even function:

Odd function:
Section #2: Formulas/Equations/Rules

When two conjugates are multiplied together, you always get a positive ___________ number.

If the roots are imaginary, they will be _____________________ of each other.

Powers of i repeat in a definite cycle:
i0 = ____
i1 = ___
i2 = ____
i3 = ____
Discriminant Rules: Complete the chart below!
If the discriminant is
The roots will be
The graph will look like
(sketch it)
A negative number
There are no x-intercepts.
zero
There is one x-intercept.
Positive perfect
square
There are two x-intercepts.
Positive non-perfect
square
There are two x-intercepts.
Example: Given the equation: x 2  2 x  8  0
a) Describe the nature of the roots.
b) Solve the equation.
c) Sketch the graph.
Transformation Rules: Use f(x) = x2 as the parent function.
Explain the vertical and or horizontal shift for each:
g(x) = x 2  4
h(x) = x 2  5
k(x) = ( x  3) 2
Explain the reflection for each:
p(x) =  x 2
j(x) = ( x  6) 2
r(x) = ( x) 2
Explain the vertical AND horizontal dilation for each:
Graph each to show the vertical vs. horizontal dilation
a)
b)
Transformation: __________________________
Transformation: __________________________
c)
d)
Transformation: __________________________
Transformation: __________________________
Evaluating Even and odd functions:
f(x) = x4
f(x) = x5
Section #3: Key methods and concepts –Complete these specific examples!!!

How to simplify radicals (Write out the detailed steps for each example)
3
4
48
48
48

How to add, subtract, multiply, divide radicals (rationalize denominator)
23 x4  3 125x7

3
9x2  3 6x2
3
8x  3 16 x  3 27 x
How do you rationalize a denominator using the conjugate
3 2
45 2

How to solve an equation containing a radical by isolating the radical
4r - 4  4  r

How to simplify negative radicals
Always simplify negative radicals in terms of i
Examples:

4 
18 
How to add, subtract, multiply complex numbers
Treat i as a normal variable, but always simplify powers of i
Example:
(3  4i )  (6  3i ) 

How to simplify
(3  i )( 4powers
 i )  of i
If a whole number exponent is divided by 4, the remainder is 0, 1, 2, or 3.
We can simplify powers of i by using the remainders after dividing by 4.
Examples:

i 105 =
Multiplying conjugate pairs
(5 + 3i)( 5 - 3i)=

How to graph a complex number
Graph on a coordinate plane where the x axis is the real part and the y axis is
the imaginary part.
Example: Graph
-3+4i
i i64=