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The farther a slope is away from zero, the _______ it will be.
Narrower
Example: 10 will be 10 integers away from zero, compared to a slope of 1 (only one integer away). 10 will be narrower.
Same thing with negatives: -10 will be 10 integers away from zero. A slope of -1 will only be one integer away. -10 will be narrower.
The closer a slope is to zero, the _________ it will be.
Wider
Example: 10 will be 10 integers away from zero, compared to a slope of 1 (only one integer away). 10 will be narrower.
Same thing with negatives: -10 will be 10 integers away from zero. A slope of -1 will only be one integer away. -10 will be narrower.
How do you find c in completing a square?
b/2^2
How do we know if something if isn’t a function?
It doesn’t pass the Vertical Line Test/Has repeating x values.
What circle do you use for the greater than or equal to sign, and less than or equal to sign.
Closed
What circle do you use for the less than and greater than symbols?
Open
Transformation: INSIDE- positive ? negative?
Positive = Left
Negative = Right
Transformation: OUTSIDE- positive? negative?
Positive = Up
Negative = Down
Natural numbers are
Positive Integers
Commutative Property
The order doesn’t matter
Example: 5 + 4 = 4 + 5 = 9
Associative Property
Grouping doesn’t matter
Example: (1 + 2) + 3 = 1 + (2 + 3) = 6
Distributive Property
Numbers outside are multiplied by terms inside ()
Example: 3(x + y) = 3x + 3y
Additive Identity
Anything plus 0 equals itself.
Example: x + 0 = x
Multiplicative Identity
Anything times one is itself
Example: 1 * x = x
Additive Inverse
When we add inverses, the sum is 0
Example: -2 + 2 = 0
Multiplicative Inverse
When we multiply inverses, the product is one.
Example: 4 times 1/4 = 1
What does FOIL stand for?
First, Outside, Inside, Last
Used when multiplying two binomials.
Ex: (x + y) (x + y)
Multiply the first numbers, then outside numbers, inside numbers, last numbers.
Lastly, add like terms.
How do you find if a solution is one a line?
Plug in the coordinates you are given to the solution you are also given.
What’s the purpose of point slope form?
To find the slope and a point on the graph.
What’s the formula for point slope form?
y - y1 = m(x - x1)
What is point intercept form?
y = mx + b
What’s the formula for rise over run/ slope?
m = y2 - y1/ x2 - x1
f(x) = x
Linear
f(x) = x^2
Quadratic
f(x) = x^3
Cubic
f(x) = √x
Square Root
f(x) = | x |
Absolute Value
What kind of solution is this: x = 4
One solution
What kind of solution is this: -3 = -3
Infinite Solutions
What kind of solution is this? 5 = 6
No solutions
You cannot ____ exponents.
Add
Example: x^2 + x^3 doesn’t equal x^5
When using the calculator to determine if something is true or false… What number is false?
0
When using the calculator to determine if something is true or false… What number is true?
0
Graphing inequalities: If the sign eats y shade….
UP/ABOVE
Dash the lines
How do you write set notation?
{variable symbol type of number | description}
example: {x € IR | x < 0}
When declarations are separated by “and”, ____ need to be correct to be true.
Both/All statements
When declarations are separated by “or”, ____ need to be correct to be true.
Only one of them
Intersecting Lines are what kind of solution?
One solution
Parallel Lines are what kind of solution?
No Solution
What does the same line say about what kind of solution we are looking at?
Infinite Solutions
How do you do Substitution?
Isolate y for one equation
Substitute y
Solve for x
Solve for y
How do you do Elimination?
1.) Make sure the equations are lined up
2.) Add or subtract the equations to eliminate the variable with common coefficients
3.) Solve for the remaining variable
4.) Substitute your answer into either original equation and solve for the other variable
Process to solve system of equation applications
1.) Define your two variables
2.) Write a system of equations using given information
3.) Solve the system
4.) Answer word-ly
Integer Sequences: How do I know if I’m looking at a linear sequence? What do we include in linear recursive formulas
Same 1st Differences; has a coefficient: n
Integer Sequences: How do I know if I’m looking at a quadratic sequence? What do we include in quadratic recursive formulas?
Same 2nd Differences; has a ^2 exponent (squared)
Integer Sequences: How do I know if I’m looking at a exponential sequence? What do we include in linear recursive formulas?
Same ratio (multiplying a constant number); has an exponent
Explicit Formulas: A1 means?
First term
Explicit Formulas: d means?
Difference
Note
Flashcard