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