﻿ Algebra Formula

### Algebra Formula

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Category: Mathematics
• ### Ankit Kumar Sharma

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• Algebra Formulas Geometry Quadratic Equation Equation of a circle: ()( ) 2 2 2r k y h x= − + − , 0 2 = + +c bx ax Center = () k h, , Radius = r Quadratic Function: cbx ax y + + = 2 , Quadratic Formula Vertex = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − a b c a b 4 , 2 2 aac b b x 24 2− ± − = Distance Formula: ()( ) 2 1 2 2 1 2 y y x x d− + − = Slope: 1 21 2x xy y m − − =, Parallel lines: 2 1m m= , Perpendicular lines:= 2 1 1 m m− = Point-Slope Formula: () 1 1x x m y y− = − Slope-Intercept Form: b mx y+ =, Horizontal Line: y = b, Vertical Line: x = a (m = 0) (m undefined) Standard Form: CBy Ax= + Midpoint Formula: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛+ + 2 , 22 1 2 1y y x x Factoring Difference of Squares: Perfect Square Binomials: ()() b a b a b a+ − = − 2 2 (1) ( ) 2 2 2 2b ab a b a+ + = + (2) ( ) 2 2 2 2b ab a b a+ − = − Difference of Cubes () ( )2 2 3 3b ab a b a b a+ + − = − Perfect Cube Binomials Sum of Cubes (1) ( ) 3 2 2 3 3 3 3b ab b a a b a+ + + = + () ( )2 2 3 3b ab a b a b a+ − + = + (2) ( ) 3 2 2 3 3 3 3b ab b a a b a− + − = − Exponents/Radicals Imaginary Number Absolute Value n m n m b b b + = ⋅ () 0 b , 1 0 ≠ = b 1− = i () mn n mb b= () n n nb a ab= () () a x a x a xa x aa x a x a xa x or a x a xa Fora ax if xx if x x > − < ⇔ >< < − ⇔< − > ⇔ <= − = ⇔ => =⎩ ⎨ ⎧ < −≥ = or and , 00 ,0 , 2 1 4= i n nb b= − 1 n nb b 1 = mn m nb b= n n nb a ab= () 0 ,≠ =b ba ba n n n 1 2 − = i i i− = 3 n n a b ba ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − n nb b1 = − n m n m b b b − = nn nba ba = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
• 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 90 o (right) angles and four equal sides. A = s 2 P = 4s P = B + s 1 + s 2 3. Rectangle : A quadrilateral with four 90 o (right) angles. 4. Right Triangle : triangle with a 90 o (right) angle A = L x W P = 2L + 2W P = A +B +C Pythagorean Theorem 5. Parallelogram : A quadrilateral with equal opposite sides. A2 + B 2 = C 2 A = B x h P = 2B + 2s 6. Trapezoid : A quadrilateral with exactly one pair of parallel sides. () 2 1 2 1 B B h A+ = and P = B 1 + B 2 + s 1 + s 2 7. Circle : A set of points a constant distance (radius) from a given point (center). s s s s W (width) L (length ) B (base) h (height) s B2 (base) B 1 (base) h (height) s 1 s 2 Diameter (d) (distance across the circle) Radius (r) (distance from center to circle) center Circumference (C) ( distance around the circle ) 2r Aπ= r Cπ2 = 2 2 d r r d= = or h B A⋅ = 2 1 h (height) B s1 s 2 A (Leg) B (Leg) C (Hypotenuse) B A A⋅ = 2 1

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