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PreCalc - Coggle Diagram

- - - - vertex
      - axis of symmetry
      - x-ints
      - y-int
      - domain
      - range
    - - Standard form
      - Intercept form
      - Vertex form
  - - - Root
      - x-corssing
      - P(a) = 0
      - factor
      - remainder of division
- - - - Explicit rule
- - - - The velocity vector (a, b)
        
        Speed
      - Parametric equations of a line with parameter t
        
        x=k_1 t+b_1
        
        y=k_2 t+b_2
      - Vector equations of a line
        
        (x,y)=(b_1, b_2 )+(k_1,k_2 )⋅t
      - Eliminating the parameter
        
        Get rid of the parameter "t" through substitution or elimination
        
        Write in rectangular form aka in terms of x and y
    - - Vector (向量): magnitude and direction
        
        Draw a vector from a starting point
      - Dot product
        
        a=(a_x, a_y ), b=(b_x, b_y ), a ⋅b=a_x×b_x+a_y×b_y
      - Angle between vectors
        
        a⋅b=|a| × |b| × cos⁡(θ)
        
        cos⁡(θ)=(a⋅b)/(|a| × |b|)
        
        Perpendicular vectors
        
        a⋅b=0
        
        Parallel vectors
        
        a=k × b
        
        b=k × a
    - - Vertical motion (in feet)
        
        h(t)=−16t^2+v_0 t+s_0
        
        Velocity: rate of change of displacement
        
        Is the derivative of h(t) aka v(t) = h'(t)
        
        v(t)=−32t+v_0
        
        Acceleration: rate of change of velocity
        
        Is the derivative of v(t) aka a = v'(t)
        
        a=−32 feet per second squared
    - - t_1 (x_1,y_1 ) t_2 (x_2,y_2)
      - (x,y)=(x_1,y_1 )+(x_2 −x_1, y_2 −〖 y〗_1 ) (t−t_1)/(t_2−t1 ), 〖 t〗!≤t≤t_2
    - - Parametric equation for circle
      - Parametric equation for parabolas
      - Parametric equation for ellipses
      - Simplify to rectangular form
      - Change moving direction in parametric form
        
        List a table of 0,π/2, π,3π/2, 2π, observe the movement of x direction and y direction, decide which one to flip