SYMKC Algebra 1

|-a|

a

|a|

a

Associative Addition Property

a + (b + c) = (a + b) + c

Commutative Addition Property

a + b = b + a

Distributive Property

a(b+c) = ab + ac

Associative Multiplication Property

a*(b*c) = (a*b)*c

Commutative Multiplication Property

a*b = b*a

Pythagorean Theorem

a^2 + b^2 = c^2

(Linear) Standard Form

ax + by = c

Discrimination Formula

b^2 - 4ac

Distance Formula

d = sqrt[(Δx)^2 + (Δy)^2]

Distance formula (physics)

d =r*t

>

greater than

≥

greater than or equal to

10^3

1000

2^10

1024

4^5

1024

5!

120

5^3

125

2^7

128

11^3

1331

2^4

16

13^2

169

12^3

1728

14^2

196

2!

2

2^11

2048

6^3

216

15^2

225

4!

24

3^5

243

16^2

256

2^8

256

4^4

256

3^3

27

17^2

289

5^5

3125

2^5

32

18^2

324

7^3

343

(Quadratic) Vertex

(h,k)

Midpoint Formula

(m1, m2) = ((x1 + x2)/2, (y1 + y2)/2)

Slope

(y2 - y1)/(x2 - x1)

0!

1

1!

1

Three ways to solve a system of equations

1. Graphing 2. Substitution 3. Elimination or matrices

Order of Operations

1. Parentheses 2. Exponents 3. Multiplication/Division 4. Addition/Subtraction

19^2

361

20^2

400

2^12

4096

21^2

441

22^2

484

7!

5040

2^9

512

8^3

512

23^2

529

24^2

576

3!

6

25^2

625

5^4

625

2^6

64

4^3

64

6!

720

9^3

729

2^3

8

3^4

81

Nature of roots

>0: 2 real roots <0: 2 imaginary roots =0: 1 real root

Roots

A number at which a polynomial has the value zero, where rhe graph crosses the x-axis

Direct Variation

A relationship between to variables in which one is a constant multiple of the other y = kx

Indirect Variation

A relationship between two variables in which the product is a constant y = k/x

Mean

Arithmetic mean or average

Range

The difference between the largest and smallest numbers

Median

The middle number when a set of numbers are put in order

Mode

The number that occurs the most often in a list

Function

The relation for which each element of the domain correspond to exactly one element of the range

Domain

The set of all possible input values (usually x)

Range

The set of all possible output values (usually y)

<

less than

≤

less than or equal to

Perpendicular line slope (if y = mx + b)

m1 = -1/m2

Parallel line slope (if y = mx + b)

m1 = m2

Axis of Symmetry

x = -b/2a

Quadratic Formula

x = [-b±sqrt(b^2 - 4ac)]/2a

Point-Slope Form

y - y1 = m (x - x1)

(Quadratic) Standard Form

y = a(x-h)^2 + k

(Quadratic) Intercept Form

y = a(x-p)(x-q)

(Quadratic) General Form

y = ax^2 + bx + c

Slope-Intercept Form

y = mx + b

(Linear) Parent Function

y = x

(Quadratic) Parent Function

y = x^2