SYMKC Algebra 1
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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
