Algebra II terms

Notation

f(x) “take whatever is in parentheses and put it in for x”

Domain

input values, x-values

Range

output values, y-values

Function

X values don’t repeat; must pass vertical line test

Even Function

Symmetric to y-axis ; f(x) = f(-x)

Odd Function

Symmetric to the origin ; f(-x) = -f(x)

Inverse f^-1

Switch x and y, then solve for new y; reflection in y = x

Piecewise Functions

Defined differently on specific intervals.

Average rate of Change

m= y/x = y2-y1/x2-x1

- f(x)

Reflection in x-axis (negate the y values)

f(-x)

Reflection in the y-axis (negate the x values)

Inside the parentheses

+c shifts left

-c shifts right

Outside the parentheses

+d shifts up

-d shifts down

When given af(x)

If a= whole number, multiply y values by a, results in a vertical

stretch

If a = fraction, vertical compression

When given f(ax)

If a = whole number, divide all x values by a. Results in a

horizontal compression

If a = fraction, divide all x values. Results in a horizontal

stretch

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Factor by GCF

Pull out GCF and leave what’s left in ( ).

Factor by DOTS

2 Perfect Squares with a subtraction sign. Factors are

conjugates of each other

Factor Trinomial a = 1

Double Bubble:

Must multiply to last term and add/subtract to middle term

If last term is -, signs are different

if last term in +, signs are the same

Factor by Grouping

GCF of 1st 2 terms, GCF of 2nd 2 terms

Factor Trinomial a > 1 (AC

Method)

Multiply the A to the C, re-write as 4 terms & factor by

Sum or difference of 2 perfect

cubes

SOAP Same, opposite, always positive

To Solve a quadratic

1. Factor

2. Complete the square

3. Quadratic Formula

Completing the Square

1. Separate the x terms from the number term

2. Take half of the middle term, square it, add it on the

inside, subtract it on the outside.

3. Write it as ( )

2= #

4. Take the square root of both sides

3. Sove for x. Don’t forget the ±

Quadratic Formula

(on reference sheet)

X = −b±√b2−4ac/2a

Vertex form

1. Complete the square

2. y = a(x − h)²+k

Vertex: (h, k)

Center Radius Form of a Circle

x²+y²=r² center (0,0)

(x-h)²+(y-k)²=r² center (h,k)

Standard Form of a Circle

x²+y²+cx+dy+e=0

Converting from standard

form into center-radius form

Complete the square

Parabola, Focus and Directrix

y = ± 1/4p (x-h)²+k

Vertex: (h, k)

(located directly in middle of focus(point) and directrix (line)

p = distance from the vertex to the focus or from the vertex to

the directrix

Recursive Form

Recursive means they want the formula in terms of the

previous term (an−1)

Arithmetic Recursive Rule

an = an-1 + d

Arithmetic Sequence

(on reference sheet)

an - a1 + (n-1) d

d = common difference= right # - left #

Geometric Recursive Rule

an = (an-1)r

Geometric Sequence

(on reference sheet)

an = a1 * r^n-1

Geometric Series

(on reference sheet)

sn = (a1 - a1 *r^n)/1-r

Even Degree Polynomials

End Behavior: Same

Odd Degree Polynomials

End Behavior: Opposite