STAAR Algebra 1 Flash Cards

• Two lines that never intersect, they are parallel (they have the same slope)
• 

• System where both equations represent the same line, they intersect at all points on the line
• 

• y = x²
• Domain: All real Numbers (
• Range  
• 

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

• y=a(1-r)t
•  

a = initial value

r = decay rate (a percent)

t = time

Domain: 0<x<

• y=a(1+r)^t
•  

a = initial value

r = growth rate (a percent)

t = time

Domain: 0<x<

• ALWAYS the x-axis (the equation y=0)
• An imaginary barrier that prevents the graph from crossing the x-axis

y=a(x-h)²+k

h is the opposite of what is in the formula

Vertex: (h, k)

Equations where the variable is the exponent   y=a(b)x

• a is the y-intercept (the number without x)
• Domain: 
• Range: 0<y< (y-int is positive), <y<0 (y-int is negative)
• Horizontal asymptote: y=0

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)

A sequence created by multiplying a constant amount

 y=a₁+(n-1)(d)

a₁– the first term

d – the common difference

n – represents a position in the pattern (ex. if n = 9 it is the 9th term)

A sequence created by multiplying a constant amount

 y=a₁(r)^n-1

a₁– the first term

r – the common ratio

n – represents a position in the pattern (ex. if n = 9 it is the 9th term)

• y = x
• Domain: All Real Numbers 
• Range: All Real Numbers 

• The X-VALUES for a given function
• The INPUT values for a given function

• The Y-VALUES for a given function
• The OUTPUT values for a given function

Data that is connected

DoLoR the RoBoT

• Domain Left to Right  __<x<__
• Range Bottom to Top  __<y<__

   

per

rate of change

attached to "x"

y per x

y = mx + b

m = slope (how much you Move)

b = y - intercept (where you Begin)

Point where the graph crosses the x-axis

when y = 0

(x, 0)

aka: Root, zero of a function, solution

Point where a graph crosses the y-axis

when x = 0

(0, y)

The beginning, initial value, starting point, first

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!

Goes down from Left to right

Goes Up from left to right

Up and Down is Undefined

• All equations:  x=#
• 

AcrOss

y = a#

• (it can be graphed in the calculator)
• 

• The point where the two graphs intersect
• 

The value or values that make the equation or inequality true

(plug in the values and see which one works)

Lowest (minimum) or highest (maximum) point of a parabola

Determines Range

• Minimum:  Range  y>k
• Maximum:  Range  y<k

  

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

The graph of a quadratic equation (y = x²)



Positive opens up, negative opens down

(0,0)

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)

"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, ROOTS ZEROS, X-INTERCEPTS

(where the graph crosses the x-axis)

 

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)

• <
• Made with the LEFT hand
• shade BELOW
• Use Solid Line or Solid Circle
• 

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

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

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

Have the same slope

Never touch

• Meet at a 90^o angle
• Slopes are flipped and switched

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

• 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)

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

• 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

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

Use the box method

Exponents that are fractions can be rewritten as roots

(x, y)

• 1st - Left or Right
• 2nd - Up or Down