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FORMULAS

PARENT FUNCTIONS
Linear:  f(x) = x
Absolute Value:  f(x) = |x|
Quadratic:  f(x) = x2

Cubic:  f(x) = x3
Square Root:  f(x) =
 √x
Cube Root:  f(x) = 3
√x
Reciprical:  f(x) = 1 / x
Exponential:  f(x) = bx
Logarithmic:  f(x) =  log(x)

LINEAR EQUATIONS
Standard Form:  Ax + By = C 
Point-Slope Formula:  y – y= m(x – x1)
Slope Formula:  m = (y2 – y1) / (x2 – x1)

QUADRATIC EQUATIONS
Standard Form:  f(x) = ax2 + bx +c 
Axis of Symmetry Formula:  x = (-b) / (2a)

Vertex Form:  f(x) = a(x – h)2 + k  { Where (h, k) is the vertex and x = h is the axis of symmetry}

ABSOLUTE VALUE
Vertex Form:  f(x) = a |x – h| + k  { Where (h, k) is the vertex and a is the slope on the right side and –a is the slope on the left side}

EXPONENTIAL
Transformation:  f(x) = (a) bx-h + k { Where h determines horizontal shift and k determines vertical shift}
Growth:  f(t) = a(1 + r)t  { Where a is the intial amount r is the growth rate and t is the time}
Decay:  f(t) = a(1 – r)t { Where a is the intial amount r is the decay rate and t is the time}

LOGARITHMIIC
logb a = x  is the logarithmic form and if move to exponential form it will be bx = a

FACTORING
Difference of Squares:  a2 + b2 = (a + b)(a – b)

Quadratic Formula:  x = [-b ± √(b2 – 4ac)] / (2a)
Difference of Cubes:  a3 – b3 = (a – b)( a2 + ab + b2)
Sum of Cubes:  a3 + b3 = (a + b)( a2 - ab + b2)

COMPLEX NUMBERS
Standard Form:  a + bi  { Where a is the real part and bi is the imaginary part}
Imaginary Numbers

i   =  √ -1        i= √-1
i2 = -1            i6 = -1
i3 = -i             i7 = -i
i4 = 1             i8 = 1
(This pattern will continue)

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