Algebra 2 Midterm

Slope of 0

Y=6 —-

Undefined slope

X=2 |

Perpendicular line slope

Opposite reciprocal

Parallel line slope

Same slope

Equation for slope given two points

Y2-y1/x2-x1

Slope intercept form

y= -3/4x + 2

Standard form

3x+4y=8

Explicit rule

Based on term number

Recursive rule

Based on previous value

Arithmetic Recursive and Explicit rules

R: n>= 2, fn=fn-1 ± d, a1= y

E: an= dn ± 0th term

Geometric Recursive and Explicit

R: n>/= 2, fn= rfn-1, a1= y

E: a1(r^n-1)

Summation notation

Last term on top, n= first term on bottom, explicit rule

How to solve a geometric sequence if given a2 and a5

a5= a2 times r^5-2

Meanings of N, An, a1, d, and r

N- shows the terms place in the sequence (n=1 for first term)

An- The actual value of the number at the nth position in the list

A1- first number in sequence

D- common difference in arithmetic sequences

R- common ratio in geometric sequences multiplied to get to next number

Arithmetic finite series equation

sn= n( a1 + an)/ 2

Arithmetic infinite series

Not possible, diverges

Geometric sequences series equation

Sn= a1 (1- (r^n)/ 1-r

Geometric Infinite Series Equation

If |1|>r diverges- if not do a1/1-r to get estimated solution

fractional exponent rule

A^m/n= the n root of a to the m

What are the 3 factors that influence what a graph looks like and how do they influence it?

A- shape (0- straight, negative- upside down) Vertical stretch if a is greater than 1, vertical compression is a is less than 1

H- side to side (positive is right, negative is left)

K- up and down

Shapes of the 5 types of graphed equations

V shape, y= a |x-h| + k

Graphing 5 types of equations

Do (h,k) to get vertex. Get x and y, plug in other numbers that make sense.

How to tell even vs odd symmetry

Even: f(-x)= f(x) (even over y axis)

Odd: f(-x)= -f(x) (double reflection)

Types of equations that are even and odd

Odd: linear, cubic, cube root

Even: quadratic, absolute value

Sum or difference of cubes equation

(X+y) (x²-xy+y²) (same sign, opposite, always positive)

How to figure out different types of factoring

Types of grouping

2 by 2- make two same terms, put numbers taken out together

3 by 1- factor, then difference of squares with last term

Negative (imaginary numbers)

4(a^-4b^4)

4a^-4b^4 if it is on the bottom of a simplifying equation because the 4 doesn’t multiply by all since they are all already multiplying each other