Algebra + Coordinate Geometry

Question 1

When are we allowed to subtract inequalities?

Answer 1

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

Question 2

When are you allowed to add ineuqalities?

Answer 2

You can add inequalities in the same direction

e.g. If a > b and c > d,

a > b

+ c > d

= (a+c) > (b+d)

Question 3

If a > b and c > d, then ac > bd - true or false?

Answer 3

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)

Question 4

x^0 =

Answer 4

1

Question 5

What happens when you divide or multiply an inequality?

Answer 5

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)

Question 6

2^4 =

Answer 6

16

Question 7

2^5 =

Answer 7

32

Question 8

2^6 =

Answer 8

64

Question 9

2^7 =

Answer 9

128

Question 10

2^8 =

Answer 10

256

Question 11

2^9 =

Answer 11

512

Question 12

What is the order of the quadrants in the coordinate plane

Answer 12

Question 13

what is the slope formula?

Answer 13

Question 14

If a line has a slope of 1 or -1, what is the angle it makes with the axes?

Answer 14

45 degress

Question 15

How do you find the slope of a perpendicular line?

Answer 15

it is the opposite sign reciprocal (swith sign and reverse numerator and denomintor)

Question 16

What is slope intercept form?

Answer 16

y = mx+b

where:

• m is the slope and
• b is the y intercept

Question 17

What is the slope of a horizontal line?

What is the slope of a vertical line?

Answer 17

horizontal: 0
vertical: undefined (it is impossible to divide by zero)

Question 18

What is point slope form?

Answer 18

Question 19

what is the distance formula?

Answer 19

Question 20

What is standard form of a quadratic function?

Answer 20

Question 21

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

Answer 21

Question 22

In vertex form, if a is negative a quadratic function _____________?

Answer 22

opens downwards

Question 23

In vertex form, if a is positive a quadratic function _____________?

Answer 23

opens upwards

Question 24

What is the midpoint formula?

Answer 24

Question 25

How do you convert a quadratic function from standard form to vertex form? What are the steps?

Answer 25

Complete the square:

1. factor ‘a’ out of the first 2 terms
2. using the coefficient for the x term, take half that number squared and then add it and subtract it *** best thing to do is subtract it all the way at the end right away so you don’t forget to multiply it by the coefficient
3. now the first 3 terms inside the parentheses form a perfect square - factor them

**Note, remember to multiply the 4th term (that isn’t part of the perfect square) that you’re subtracting by the coefficient before taking it out of the parentheses.

4. distribute the a value
5. collect like terms

Question 26

Answer 26

E = k

OR

E = -k

Question 27

What needs to be done before you can solve an abolute value equation?

Answer 27

You need to isolate the absolute value on one side of the equation

Question 28

How do you solve an aboslute value equation where there is an expression on each side?

What do you need to check for?

Answer 28

1. Is always to isolate the absolute value
2. Set what is inside the absolute value equal to the other expression and the -1(the other expression)
3. Solve
4. Check for extraneous solutions (plug into original absolute value equation)

Question 29

What operations can be performed that preserve a statement of inequality

Answer 29

1. You can add the same thing to both sides
2. You can subtract the same thing from both sides

(addition and subtraction work exactly the same way for inequalities as they do for regular equations)

Question 30

What is the rule for multiplying and dividing both sides of an inequality?

Answer 30

You can multiple or divide both sides of an inequality by any positive number, and the inequality will be preserved

BUT

If you multiply or divide both sides by a negative number, you need to switch (flip) the inequality sign to the opposite direction