Math B

Math B

1. Parabolas

   • Axis of symmetry
   • Turning point
     • Vertex form
       • (-h, k)
     • Standard form
       • ax^2 + bx + c = 0
         • x = -b/2a
   • X intercept
   • Y intercept
   • Min/Max
     • Vertex
       • Min = -k (-ve)
       • Max = k (+ve)
     • Standard
       • Max = -a (-ve)
       • Min = a (+ve)
   • End points
     • Sub values of min/max x (if given) to find y. Convert to co-ordinates.
   • Domain/Range
     • Domain = X values
     • Range = Y values
   • Graphing: --> X/y-intercept, TP

2. Periodic Functions

   • Cycle -- A single period
   • Amp -- Length from M to H/L line
   • Frequency = 1/Period
   • General form: asinb(x+c)+d
     • a = amp
     • c = horizonal displacement,
       • TO L = (+ve); TO R = (-ve)
     • d = vertical phase
     • b = 360/period
   • Predicting the peirod: x = (x + multiple * period)

3. Rates of change

   • Converting s-t to v-t graphs
     • Curved --> Diagonal line
       • Getting steeper (with increases to x)
         • +ve diagonal line
       • Not getting steeper (with increases to x)
         • -ve
     • Diagonal line --> Straight
     • Straight --> 0
   • Fixed rate = For every increase in value, the rate of change is the same.
     • Fixed rate = Quantity (1) / Quantity (2)
       • y = kx, where k is constant, x/y are quantities.
   • Average rate = 2nd value -- 1st value / time taken for change
     • SIMILAR TO: a = v - u/t (Physics)
     • Functions: f(x1) -- f(x2) / (x2) -- (x1)
     • Rate of change is... --> (-ve) falling surve, (+ve) rising curve, (0) horizontal line
   • v = d/t
     • Speed = distance/time
     • Velocity = distance/time
   • Displacement -- Body's position from origin
     • Distance -- Body's total distance from the origin
   • Tangents
     • Short chords = Greater accuracy
       • Chord = Line straight through circle
   • Limit of sequence = Values closer to final value

4. Different forms

   • Standard
     • ax^2 + bx + c = 0
   • Vertex
     • y = a(x - h)^2 + k

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