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