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