Algebra + Coordinate Geometry Flashcards
When are we allowed to subtract inequalities?
We can subtract inequalities in opposite directions
If a > b and d < c, then
a > b
- d < c
= (a-d) > (b-c)
* with the resulting inequality having the same direction as the inequality we subtracted from
When are you allowed to add ineuqalities?
You can add inequalities in the same direction
e.g. If a > b and c > d,
a > b
+ c > d
= (a+c) > (b+d)
If a > b and c > d, then ac > bd - true or false?
False - this may apply to positive numbers, but there is no general rule that applies to multiplication/division of inequalities
even if we multiply big times big and small times small, the inequalities could contain negative numbers, which makes it impossible to predict which of the products would be larger. (e.g. if the two small numbers are negative e.g. -20 and -40 their product would be a large positivie number 400)
x^0 =
1
What happens when you divide or multiply an inequality?
If you multiply or divide both sides of an inequality by a negative number, reverse the direction of the inequality sign (note, if it is positive do not reverse the sign)
2^4 =
16
2^5 =
32
2^6 =
64
2^7 =
128
2^8 =
256
2^9 =
512
What is the order of the quadrants in the coordinate plane

what is the slope formula?

If a line has a slope of 1 or -1, what is the angle it makes with the axes?
45 degress
How do you find the slope of a perpendicular line?
it is the opposite sign reciprocal (swith sign and reverse numerator and denomintor)
What is slope intercept form?
y = mx+b
where:
- m is the slope and
- b is the y intercept
What is the slope of a horizontal line?
What is the slope of a vertical line?
horizontal: 0
vertical: undefined (it is impossible to divide by zero)
What is point slope form?

what is the distance formula?

What is standard form of a quadratic function?

What is vertex form of a quadratic function? Describe all its parts.

In vertex form, if a is negative a quadratic function _____________?
opens downwards
In vertex form, if a is positive a quadratic function _____________?
opens upwards
What is the midpoint formula?

