Algebra II Midterm Study Guide

real numbers
all numbers

rational numbers
1/2, 0.3, 1, 2 2/3, -5/4, -1.07

integers
-2, -1, 0, 1, 2

whole numbers
0, 1, 2, 3

natural numbers
1, 2, 3

irrational numbers
-square root of 3, pi, cube root of 40

relation
set of pairs of input and output values

function
relation in which each element of the domain is paired with exactly on element of the range

domain
set of all inputs, or x-coordinates, of the ordered pairs

range
set of all outputs, or y-coordinates, of the ordered pairs

slope formula
y2 – y1/x2 – x1

point slope form
y – y1 = m(x – x1)

slope intercept form
y = mx + b

standard form
ax + by = c

reflective property
a = a

symmetric property
a = b then b = a

transitive property
a = b and b = c, then a = c

direct variation
y = kx, k not equal to 0

constant variation
k = y/x

absolute value function
f(x) = Imx + bI + c

vertex in absolute value function
(-b/m, c)

independent system
intersecting

dependent system
coinciding lines, no unique solution

inconsistent system
parallel lines, no solution

matrix
row x column

matrix
1st row x 1st column, 1st row x 2nd column, 2nd row x 1st column, 2nd row x 2nd column

vertex form of a quadratic function
y = a(x – h) squared + k

standard form of a quadratic equation
ax squared + bx + c

imaginary number
square root of -1

quadratic formula
x = -b +- square root of b squared – 4ac/ 2a

degree 0
constant

degree 1
linear

degree 2
quadratic

degree 3
cubic

degree 4
quartic

degree 5
quintic

sum of cubes
a cubed + b cubed = (a + b)(a squared – ab + b squared)

difference of cubes
a cubed – b cubed = (a – b)(a squared + ab + b squared)

permutation
an arrangement of items in a particular order

combination
selection in which order does not matter