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The absolute value of a number is
its distance from 0 on the nmber line
For an absolute value equation,
you must solve for both the negative value and the positive value of the number
3-x<5 and 3-x>-5
e.g. To solve |3-x|<5, set up two inequalities:
y=mx+b
Line equation
(y₂-y₁)/(x₂-x₁) or ∆y/∆x
m=(rise)/(run) is equivalent to
The midpoint of two endpoints is
the average of the x-coordinates and the average of the y-coordinates...
√(x₂-x₁)²+(y₂-y₁)²
The distance formula =
equal slope
parallel lines have
perpendicular lines have
negative reciprocal slopes
x-intercepts, roots, or zeroes
Most quadratic equations have two solutions, also known as
(x-y)(x+y)
x²-y² =
(x+y)² =
x² + 2xy + y²
(x-y)² =
x² - 2xy + y²
A quadratic function takes the form
f(x) = ax² + bx + c
up
If a > 0, the parabola opens
down
If a < 0, the parabola opens
fat
If a is a fraction, the parabola is
To quickly graph a parabola...
(a) let x=0 and find where the graph will cross the y-axis
supplementary angles =
180°, a straight line
vertical and congruent
Angles across from each other are
equal, equal
When two parallel lines are intersected by a third line, the corresponding acute angles are ________ and the corresponding obtuse angles are ________
bisects it
A line that divides an angle or another line into two equal pieces
180°
Degrees in a line
the two opposite interior angles
An exterior angle of ANY triangle is equal to the sum of the measures of
greater
In ANY triangle, a side opposite a greater angle is ______________ than a side opposite a smaller angle
also equal
In ANY triangle, sides opposite equal angles are
isosceles triangle:
a triangle with two equal sides and two corresponding equal angles
equilateral:
a triangle with three equal sides and three corresponding equal angles (each 60° in measure)
*Triangle Inequality Theorem*
every side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the other two sides
SIMILAR triangles have
EQUAL angles and PROPORTIONAL sides
Pythagorean triplets
3:4:5 and 5:12:13 and their multiples
x, x, x√2
The sides of a 45-45-90 degree triangle:
x, x√3, 2x
The sides of a 30-60-90 degree triangle: