Algebra Formulas - This is just a cheat sheet I used to use. PDF

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This is just a cheat sheet I used to use....

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Algebra Formulas Geometry Equation of a circle: (x − h )2 + ( y − k )2 = r 2 , Center = (h, k ) , Radius = r

Quadratic Function: y = ax2 + bx + c ,

Quadratic Equation ax 2 + bx + c = 0 Quadratic Formula

b ⎞ ⎛ b , c − ⎟⎟ Vertex = ⎜⎜ − 4a ⎠ ⎝ 2a 2

x=

− b ± b 2 − 4ac 2a

2 2 Distance Formula: d = (x 2 − x1 ) + ( y2 − y1 ) y − y1 1 Slope: m = 2 , Parallel lines: m1 = m2 , Perpendicular lines: m1 = − x 2 − x1 m2 Point-Slope Formula: y − y1 = m( x − x1 ) Slope-Intercept Form: y = mx + b , Horizontal Line: y = b, Vertical Line: x = a (m = 0) (m undefined) Standard Form: Ax + By = C ⎛ x + x y + y2 ⎞ Midpoint Formula: ⎜ 1 2 , 1 ⎟ 2 ⎠ ⎝ 2

Factoring Difference of Squares: a 2 − b 2 = (a − b)(a + b)

Perfect Square Binomials: 2 2 2 (1) (a + b ) = a + 2ab + b

(2) Difference of Cubes a 3 − b 3 = (a − b ) a 2 + ab + b 2

(

Sum of Cubes

(

a 3 + b 3 = (a + b ) a 2 − ab + b 2

)

(a − b)2 = a 2 − 2ab + b 2

Perfect Cube Binomials (1)

)

(2)

Exponents/Radicals b 0 = 1, (b ≠ 0) b ⋅b n = b m+ n m

(a + b)3 = a 3 + 3a 2b + 3ab 2 + b 3 (a − b)3 = a 3 − 3a 2b + 3ab 2 − b 3 Imaginary Number i = −1

i = −1 2

(b )

m n

=b

mn

bm = b m− n n b 1 b− n = n b

1 b n

b

−n

= bn

b =b n

m

(ab )

n

= b

n

n

⎧ x, if x ≥ 0 x =⎨ ⎩− x , if x < 0

i = −i

a = a2

i4 = 1

For a > 0,

3

n

an ⎛a ⎞ ⎜ ⎟ = n b ⎝b ⎠ ⎛a ⎞ ⎜ ⎟ ⎝b ⎠

−n

⎛b⎞ =⎜ ⎟ ⎝a⎠

n

n

ab = n a n b

n

a na = , (b ≠ 0) b nb

1 n

m

=a b n

Absolute Value

x = a ⇔ x = − a or x = a x < a ⇔ (x > −a and x < a ) ⇔ (− a < x < a ) x > a ⇔ x < − a or x > a

Area & Perimeter Formulas Area (A) is the amount of square units of space an object occupies. Perimeter (P) is the distance around a figure. 1. Square: A quadrilateral (4-sided figure) 2. Triangle: A 3-sided figure with four 90o (right) angles and four equal sides.

s A = s2

s

s

s1 h

P = 4s

Rectangle:

A quadrilateral with four 90o (right) angles.

1 B⋅h 2

P = B + s1 + s2

(height)

s 3.

A=

s2

B Right Triangle: triangle with a 90o (right)

4.

angle

A=LxW

W

C (Hypotenuse)

A (Leg)

(width)

P = 2L + 2W

B (Leg)

Parallelogram: A quadrilateral with equal opposite sides. s

1 A⋅B 2

P = A +B +C

L (length) 5.

A=

Pythagorean Theorem 2 2 2

A +B =C

A=Bxh P = 2B + 2s

h (height)

B (base) 6.

Trapezoid: A quadrilateral with exactly one pair of parallel sides. B1 (base) s1

h (height)

s2

1 h( B1 + B2 ) and 2 P = B1 + B2 + s1 + s2 A=

B2 (base) 7.

Circle: A set of points a constant distance (radius) from a given point (center). Radius (r)

A = πr

2

C = 2πr d d = 2 r or r = 2

Diameter (d) (distance across the circle)

center

(distance from center to circle)

Circumference (C) (distance around the circle)...