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System of Equations with No Solution
 Two lines that never intersect, they are parallel (they have the same slope)

System of equations with infinite solutions
 System where both equations represent the same line, they intersect at all points on the line

Quadratic Parent Function
 y = x^{2}
 Domain: All real Numbers (
 Range
 ^{}

Parent Function
 The most basic graph (no shifts, stretches, etc.).
 *Must go through the origin*
 *Must be positive*

Exponential Decay
a = initial value
r = decay rate (a percent)
t = time
Domain: 0<x<

Exponential Growth
a = initial value
r = growth rate (a percent)
t = time
Domain: 0 <x<

Horizontal Asymptote
 ALWAYS the xaxis (the equation y=0)
 An imaginary barrier that prevents the graph from crossing the xaxis

Vertex Form of a Quadratic
y=a(xh)^{2}+k
h is the opposite of what is in the formula
Vertex: (h, k)


Evaluating Functions
If f(x)=3x+5, find f(2)
 Plug in 2 for x
 f(2)=3(2)+5
 f(2)=6+5
 f(2)=11
 Same thing as (2,11)

Arithmetic Sequence
A sequence created by multiplying a constant amount
y=a_{1}+(n1)(d)
a_{1}– the first term
d – the common difference
n – represents a position in the pattern (ex. if n = 9 it is the 9th term)

Geometric Sequence
A sequence created by multiplying a constant amount
y=a_{1}(r)^{n1}
a_{1}– the first term
r – the common ratio
n – represents a position in the pattern (ex. if n = 9 it is the 9th term)


Domain
 The XVALUES for a given function
 The INPUT values for a given function

Range
 The YVALUES for a given function
 The OUTPUT values for a given function

Continuous Data
Data that is connected
DoLoR the RoBoT
 Domain Left to Right __<x<__
 Range Bottom to Top __<y<__

Slope
per
rate of change
attached to "x"
y per x

Equation of a line
y = mx + b
m = slope (how much you Move)
b = y  intercept (where you Begin)

X  intercept
Point where the graph crosses the xaxis
when y = 0
(x, 0)
aka: Root, zero of a function, solution

Y  intercept
Point where a graph crosses the yaxis
when x = 0
(0, y)
The beginning, initial value, starting point, first

Negative Exponents
To make an exponent positive, move it to either the top or bottom (the opposite of where it starts at).
Remember: Negative exponents are unhappy so we must MOVE them to make them happy!

Negative Slope
Goes down from Left to right

Positve Slope
Goes Up from left to right

Undefined slope
Up and Down is Undefined
 All equations: x=#

Zero Slope
Acr Oss
y = a#
 (it can be graphed in the calculator)

Solution to a system of equations
 The point where the two graphs intersect

Solving equations
The value or values that make the equation or inequality true
(plug in the values and see which one works)

Vertex
Lowest (minimum) or highest (maximum) point of a parabola
Determines Range
 Minimum: Range y>k
 Maximum: Range y<k

Direct Variation
Change it to "divided by"  its the same thing as slope!


Parabola
The graph of a quadratic equation (y = x ^{2})
Positive opens up, negative opens down

Origin
(0,0)

y=(xc)+d
c is INSIDE so its a horitzontal transfomration
 +c  move left
 c  move right
d is outside the parentheses so its a vertical shift
 +d  move up
 d  move down

a is INSIDE so its a HORIZONTAL stretch/compress
a > 1  Horizontal COMPRESSION of 1/a
0<a<1 (means a is between 0 and 1)  Horizontal Stretch of 1/a
HIO (Horizontal Inside Opposite)

y=ax^{2}
"a" stretches/compresses the graph  a is OUTSIDE so its effects the graph vertically
a > 1  Vertical STRETCH
0<a<1 (means a is between 0 and 1)  Vertical COMPRESSION


Solutions of a quadratic equation
SOLUTIONS, ROOTS ZEROS, XINTERCEPTS
(where the graph crosses the xaxis)

perimeter
The distance around the outside of a figure
How to find it: Add up all the sides
(in a circle, it is called the circumference)

Less than or equal to
 <
 Made with the LEFT hand
 shade BELOW
 Use Solid Line or Solid Circle

Less than
 <
 Made with the LEFT hand
 shade BELOW
 Use Dashed Line or Open Circle

Greater Than or Equal To
 >
 Made with the RIGHT hand
 shade ABOVE
 Use Dashed Line or Open Circle

Greater than
 >
 Made with the RIGHT hand
 shade ABOVE
 Use Dashed Line or Open Circle

Parallel lines
Have the same slope
Never touch

Perpendicular lines
 Meet at a 90^{o} angle
 Slopes are flipped and switched

Line of symmetry
A line that can be drawn through a figure that causes both sides to look identical

function
 The x’s don’t repeat!!!
 Passes the vertical line test
 (if you draw a vertical line anywhere on the graph it only touches the graph once)

Dependent Variable
(dependent quantity)
 Y
 Variable who’s value DEPENDS on another variable
 (must be an unknown)
 What occurs second

Independent Variable
(independent quantity)
 X
 Variable who’s value can be chosen
 If given an equation, it is the variable IN the equation
 (must be an unknown)
 What occurs first

Discrete Data
 Data that is disconnected.
 Written as {1, 2, 3, 4, 5}
 Ex: Counting

Multiplying Polynomials
Use the box method

Rational Exponents
Exponents that are fractions can be rewritten as roots

Plotting Points
(x, y)
 1st  Left or Right
 2nd  Up or Down

