Algebra 2 And Trigonometry Formulae

FORMULA PAGE 1 FOIL: Firsts, Outsides, Insides, Lasts Parabola (Quadratic Equation) Forms Standard: Factored:

y = ax 2 + bx + c y = a ( x − r1 )( x − r2 ) y = a( x − h ) + k 2

Vertex:

Quadratic Formula:

− b ± b2 − 4 ⋅ a ⋅ c x= 2⋅a Gravitational Acceleration of a Falling Object:

1 h = − ⋅ g ⋅ t 2 + v0 ⋅ t + h0 , where g = 32 ft/s/s = 9.8 m/s/s 2 Matrix Multiplication = rows times columns (The product of an l x m matrix times an m x n matrix will be an l x n matrix.)

Determinant:

a b  det  = ad − bc  c d 

Matrix Inverse:

a b  c d   

−1

=

1  d − b ad − bc − c a 

FORMULA PAGE 2 c2 = a 2 + b2

The Pythagorean Theorem Trigonometry

Law of Sines:

SOHCAHTOA

sin A sin B sin C = = a b c

Law of Cosines:

c 2 = a 2 + b 2 − 2ab cos( C )

Radians/Degrees Conversion:

Polar/Cartesian Conversion: Unit Circle with an angle:

π 180 or 180 π

( x, y ) = ( r cos θ , r sin θ )

( x, y ) = ( cosθ , sin θ ) ; slope = tangent

General Equation of a Circle:

( x − h) 2 + ( y − k ) 2 = r 2

General Equation of an Ellipse centered at the origin:

x2 y2 + 2 =1 2 a b General Equation of a Hyperbola centered at the origin:

x2 y2 − =1 a 2 b2 Population Growth Formula (General Exponential Formula):

y = a ⋅b x , where a is the initial value and b is the growth rate Exponential Decay Formula:

1 y = 100 ⋅  x 2