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Graphs of Quartic Polynomial Functions

Let's analyze the following polynomial function.

f(x) = FUNCTION 
      = SIMPLIFIED_FUNCTION  (obtained on multiplying the terms)

You might also be interested in reading about quadraticcubic functions 
Let us analyze the graph of this function which is a quartic polynomial. A quartic polynomial is a fourth degree polynomial. 
  • These have zero to four real roots
  • They may have one, two or three extrema (maxima/minima - turning points)
  • Zero, one or two inflection (inflexion) points.
Let's do some curve sketchingy = f(x) = FUNCTION = SIMPLIFIED_FUNCTION

We can plot the curve by computing some sample points other than the zeroes already known. 
Some sample points are: SAMPLE_POINTS 




This graph cuts the x-axis at: 
NOTE_ON_ROOTS

These values of x are the roots of the quadratic equation FUNCTION = 0  

Let us analyze the turning points in this curve. 
The derivative of the given function = f'(x) = DERIVATIVE
This is a cubic function. 
Turning points are those where the derivative of the function (obtained on differentiating the function) is zero. 
These may be obtained by solving the cubic equation DERIVATIVE = 0.
NOTE_ON_TURNING_POINTS.

Now, let us take a look at the inflexion
These are the points where the curve changes concavity. 
The second derivative f'''(x) = SECOND_DERIVATIVE
This is a quadratic function. The value(s) of x for which this quadratic function is zero, are the inflexion points. 
NOTE_ON_INFLEXION_POINTS




Graph of a Quartic Function with zeros at (-15,-20,-20,-5)
Graph of a Quartic Function with zeros at (-15,-20,-20,-2)
Graph of a Quartic Function with zeros at (-15,-20,-20,1)
Graph of a Quartic Function with zeros at (-15,-20,-20,4)
Graph of a Quartic Function with zeros at (-15,-20,-13,-5)
Graph of a Quartic Function with zeros at (-15,-20,-13,-2)
Graph of a Quartic Function with zeros at (-15,-20,-13,1)
Graph of a Quartic Function with zeros at (-15,-20,-13,4)
Graph of a Quartic Function with zeros at (-15,-20,-6,-5)
Graph of a Quartic Function with zeros at (-15,-20,-6,-2)
Graph of a Quartic Function with zeros at (-15,-20,-6,1)
Graph of a Quartic Function with zeros at (-15,-20,-6,4)
Graph of a Quartic Function with zeros at (-15,-20,1,-5)
Graph of a Quartic Function with zeros at (-15,-20,1,-2)
Graph of a Quartic Function with zeros at (-15,-20,1,1)
Graph of a Quartic Function with zeros at (-15,-20,1,4)
Graph of a Quartic Function with zeros at (-15,-20,8,-5)
Graph of a Quartic Function with zeros at (-15,-20,8,-2)
Graph of a Quartic Function with zeros at (-15,-20,8,1)
Graph of a Quartic Function with zeros at (-15,-20,8,4)
Graph of a Quartic Function with zeros at (-15,-20,15,-5)
Graph of a Quartic Function with zeros at (-15,-20,15,-2)
Graph of a Quartic Function with zeros at (-15,-20,15,1)
Graph of a Quartic Function with zeros at (-15,-20,15,4)
Graph of a Quartic Function with zeros at (-15,-12,-20,-5)
Graph of a Quartic Function with zeros at (-15,-12,-20,-2)
Graph of a Quartic Function with zeros at (-15,-12,-20,1)
Graph of a Quartic Function with zeros at (-15,-12,-20,4)
Graph of a Quartic Function with zeros at (-15,-12,-13,-5)
Graph of a Quartic Function with zeros at (-15,-12,-13,-2)
Graph of a Quartic Function with zeros at (-15,-12,-13,1)
Graph of a Quartic Function with zeros at (-15,-12,-13,4)
Graph of a Quartic Function with zeros at (-15,-12,-6,-5)
Graph of a Quartic Function with zeros at (-15,-12,-6,-2)
Graph of a Quartic Function with zeros at (-15,-12,-6,1)
Graph of a Quartic Function with zeros at (-15,-12,-6,4)
Graph of a Quartic Function with zeros at (-15,-12,1,-5)
Graph of a Quartic Function with zeros at (-15,-12,1,-2)
Graph of a Quartic Function with zeros at (-15,-12,1,1)
Graph of a Quartic Function with zeros at (-15,-12,1,4)
Graph of a Quartic Function with zeros at (-15,-12,8,-5)
Graph of a Quartic Function with zeros at (-15,-12,8,-2)
Graph of a Quartic Function with zeros at (-15,-12,8,1)
Graph of a Quartic Function with zeros at (-15,-12,8,4)
Graph of a Quartic Function with zeros at (-15,-12,15,-5)
Graph of a Quartic Function with zeros at (-15,-12,15,-2)
Graph of a Quartic Function with zeros at (-15,-12,15,1)
Graph of a Quartic Function with zeros at (-15,-12,15,4)
Graph of a Quartic Function with zeros at (-15,-4,-20,-5)
Graph of a Quartic Function with zeros at (-15,-4,-20,-2)
Graph of a Quartic Function with zeros at (-15,-4,-20,1)
Graph of a Quartic Function with zeros at (-15,-4,-20,4)
Graph of a Quartic Function with zeros at (-15,-4,-13,-5)
Graph of a Quartic Function with zeros at (-15,-4,-13,-2)
Graph of a Quartic Function with zeros at (-15,-4,-13,1)
Graph of a Quartic Function with zeros at (-15,-4,-13,4)
Graph of a Quartic Function with zeros at (-15,-4,-6,-5)
Graph of a Quartic Function with zeros at (-15,-4,-6,-2)
Graph of a Quartic Function with zeros at (-15,-4,-6,1)
Graph of a Quartic Function with zeros at (-15,-4,-6,4)
Graph of a Quartic Function with zeros at (-15,-4,1,-5)
Graph of a Quartic Function with zeros at (-15,-4,1,-2)
Graph of a Quartic Function with zeros at (-15,-4,1,1)
Graph of a Quartic Function with zeros at (-15,-4,1,4)
Graph of a Quartic Function with zeros at (-15,-4,8,-5)
Graph of a Quartic Function with zeros at (-15,-4,8,-2)
Graph of a Quartic Function with zeros at (-15,-4,8,1)
Graph of a Quartic Function with zeros at (-15,-4,8,4)
Graph of a Quartic Function with zeros at (-15,-4,15,-5)
Graph of a Quartic Function with zeros at (-15,-4,15,-2)
Graph of a Quartic Function with zeros at (-15,-4,15,1)
Graph of a Quartic Function with zeros at (-15,-4,15,4)
Graph of a Quartic Function with zeros at (-15,4,-20,-5)
Graph of a Quartic Function with zeros at (-15,4,-20,-2)
Graph of a Quartic Function with zeros at (-15,4,-20,1)
Graph of a Quartic Function with zeros at (-15,4,-20,4)
Graph of a Quartic Function with zeros at (-15,4,-13,-5)
Graph of a Quartic Function with zeros at (-15,4,-13,-2)
Graph of a Quartic Function with zeros at (-15,4,-13,1)
Graph of a Quartic Function with zeros at (-15,4,-13,4)
Graph of a Quartic Function with zeros at (-15,4,-6,-5)
Graph of a Quartic Function with zeros at (-15,4,-6,-2)
Graph of a Quartic Function with zeros at (-15,4,-6,1)
Graph of a Quartic Function with zeros at (-15,4,-6,4)
Graph of a Quartic Function with zeros at (-15,4,1,-5)
Graph of a Quartic Function with zeros at (-15,4,1,-2)
Graph of a Quartic Function with zeros at (-15,4,1,1)
Graph of a Quartic Function with zeros at (-15,4,1,4)
Graph of a Quartic Function with zeros at (-15,4,8,-5)
Graph of a Quartic Function with zeros at (-15,4,8,-2)
Graph of a Quartic Function with zeros at (-15,4,8,1)
Graph of a Quartic Function with zeros at (-15,4,8,4)
Graph of a Quartic Function with zeros at (-15,4,15,-5)
Graph of a Quartic Function with zeros at (-15,4,15,-2)
Graph of a Quartic Function with zeros at (-15,4,15,1)
Graph of a Quartic Function with zeros at (-15,4,15,4)
Graph of a Quartic Function with zeros at (-15,12,-20,-5)
Graph of a Quartic Function with zeros at (-15,12,-20,-2)
Graph of a Quartic Function with zeros at (-15,12,-20,1)
Graph of a Quartic Function with zeros at (-15,12,-20,4)
Graph of a Quartic Function with zeros at (-15,12,-13,-5)
Graph of a Quartic Function with zeros at (-15,12,-13,-2)
Graph of a Quartic Function with zeros at (-15,12,-13,1)
Graph of a Quartic Function with zeros at (-15,12,-13,4)
Graph of a Quartic Function with zeros at (-15,12,-6,-5)
Graph of a Quartic Function with zeros at (-15,12,-6,-2)
Graph of a Quartic Function with zeros at (-15,12,-6,1)
Graph of a Quartic Function with zeros at (-15,12,-6,4)
Graph of a Quartic Function with zeros at (-15,12,1,-5)
Graph of a Quartic Function with zeros at (-15,12,1,-2)
Graph of a Quartic Function with zeros at (-15,12,1,1)
Graph of a Quartic Function with zeros at (-15,12,1,4)
Graph of a Quartic Function with zeros at (-15,12,8,-5)
Graph of a Quartic Function with zeros at (-15,12,8,-2)
Graph of a Quartic Function with zeros at (-15,12,8,1)
Graph of a Quartic Function with zeros at (-15,12,8,4)
Graph of a Quartic Function with zeros at (-15,12,15,-5)
Graph of a Quartic Function with zeros at (-15,12,15,-2)
Graph of a Quartic Function with zeros at (-15,12,15,1)
Graph of a Quartic Function with zeros at (-15,12,15,4)
Graph of a Quartic Function with zeros at (-6,-20,-20,-5)
Graph of a Quartic Function with zeros at (-6,-20,-20,-2)
Graph of a Quartic Function with zeros at (-6,-20,-20,1)
Graph of a Quartic Function with zeros at (-6,-20,-20,4)
Graph of a Quartic Function with zeros at (-6,-20,-13,-5)
Graph of a Quartic Function with zeros at (-6,-20,-13,-2)
Graph of a Quartic Function with zeros at (-6,-20,-13,1)
Graph of a Quartic Function with zeros at (-6,-20,-13,4)
Graph of a Quartic Function with zeros at (-6,-20,-6,-5)
Graph of a Quartic Function with zeros at (-6,-20,-6,-2)
Graph of a Quartic Function with zeros at (-6,-20,-6,1)
Graph of a Quartic Function with zeros at (-6,-20,-6,4)
Graph of a Quartic Function with zeros at (-6,-20,1,-5)
Graph of a Quartic Function with zeros at (-6,-20,1,-2)
Graph of a Quartic Function with zeros at (-6,-20,1,1)
Graph of a Quartic Function with zeros at (-6,-20,1,4)
Graph of a Quartic Function with zeros at (-6,-20,8,-5)
Graph of a Quartic Function with zeros at (-6,-20,8,-2)
Graph of a Quartic Function with zeros at (-6,-20,8,1)
Graph of a Quartic Function with zeros at (-6,-20,8,4)
Graph of a Quartic Function with zeros at (-6,-20,15,-5)
Graph of a Quartic Function with zeros at (-6,-20,15,-2)
Graph of a Quartic Function with zeros at (-6,-20,15,1)
Graph of a Quartic Function with zeros at (-6,-20,15,4)
Graph of a Quartic Function with zeros at (-6,-12,-20,-5)
Graph of a Quartic Function with zeros at (-6,-12,-20,-2)
Graph of a Quartic Function with zeros at (-6,-12,-20,1)
Graph of a Quartic Function with zeros at (-6,-12,-20,4)
Graph of a Quartic Function with zeros at (-6,-12,-13,-5)
Graph of a Quartic Function with zeros at (-6,-12,-13,-2)
Graph of a Quartic Function with zeros at (-6,-12,-13,1)
Graph of a Quartic Function with zeros at (-6,-12,-13,4)
Graph of a Quartic Function with zeros at (-6,-12,-6,-5)
Graph of a Quartic Function with zeros at (-6,-12,-6,-2)
Graph of a Quartic Function with zeros at (-6,-12,-6,1)
Graph of a Quartic Function with zeros at (-6,-12,-6,4)
Graph of a Quartic Function with zeros at (-6,-12,1,-5)
Graph of a Quartic Function with zeros at (-6,-12,1,-2)
Graph of a Quartic Function with zeros at (-6,-12,1,1)
Graph of a Quartic Function with zeros at (-6,-12,1,4)
Graph of a Quartic Function with zeros at (-6,-12,8,-5)
Graph of a Quartic Function with zeros at (-6,-12,8,-2)
Graph of a Quartic Function with zeros at (-6,-12,8,1)
Graph of a Quartic Function with zeros at (-6,-12,8,4)
Graph of a Quartic Function with zeros at (-6,-12,15,-5)
Graph of a Quartic Function with zeros at (-6,-12,15,-2)
Graph of a Quartic Function with zeros at (-6,-12,15,1)
Graph of a Quartic Function with zeros at (-6,-12,15,4)
Graph of a Quartic Function with zeros at (-6,-4,-20,-5)
Graph of a Quartic Function with zeros at (-6,-4,-20,-2)
Graph of a Quartic Function with zeros at (-6,-4,-20,1)
Graph of a Quartic Function with zeros at (-6,-4,-20,4)
Graph of a Quartic Function with zeros at (-6,-4,-13,-5)
Graph of a Quartic Function with zeros at (-6,-4,-13,-2)
Graph of a Quartic Function with zeros at (-6,-4,-13,1)
Graph of a Quartic Function with zeros at (-6,-4,-13,4)
Graph of a Quartic Function with zeros at (-6,-4,-6,-5)
Graph of a Quartic Function with zeros at (-6,-4,-6,-2)
Graph of a Quartic Function with zeros at (-6,-4,-6,1)
Graph of a Quartic Function with zeros at (-6,-4,-6,4)
Graph of a Quartic Function with zeros at (-6,-4,1,-5)
Graph of a Quartic Function with zeros at (-6,-4,1,-2)
Graph of a Quartic Function with zeros at (-6,-4,1,1)
Graph of a Quartic Function with zeros at (-6,-4,1,4)
Graph of a Quartic Function with zeros at (-6,-4,8,-5)
Graph of a Quartic Function with zeros at (-6,-4,8,-2)
Graph of a Quartic Function with zeros at (-6,-4,8,1)
Graph of a Quartic Function with zeros at (-6,-4,8,4)
Graph of a Quartic Function with zeros at (-6,-4,15,-5)
Graph of a Quartic Function with zeros at (-6,-4,15,-2)
Graph of a Quartic Function with zeros at (-6,-4,15,1)
Graph of a Quartic Function with zeros at (-6,-4,15,4)
Graph of a Quartic Function with zeros at (-6,4,-20,-5)
Graph of a Quartic Function with zeros at (-6,4,-20,-2)
Graph of a Quartic Function with zeros at (-6,4,-20,1)
Graph of a Quartic Function with zeros at (-6,4,-20,4)
Graph of a Quartic Function with zeros at (-6,4,-13,-5)
Graph of a Quartic Function with zeros at (-6,4,-13,-2)
Graph of a Quartic Function with zeros at (-6,4,-13,1)
Graph of a Quartic Function with zeros at (-6,4,-13,4)
Graph of a Quartic Function with zeros at (-6,4,-6,-5)
Graph of a Quartic Function with zeros at (-6,4,-6,-2)
Graph of a Quartic Function with zeros at (-6,4,-6,1)
Graph of a Quartic Function with zeros at (-6,4,-6,4)
Graph of a Quartic Function with zeros at (-6,4,1,-5)
Graph of a Quartic Function with zeros at (-6,4,1,-2)
Graph of a Quartic Function with zeros at (-6,4,1,1)
Graph of a Quartic Function with zeros at (-6,4,1,4)
Graph of a Quartic Function with zeros at (-6,4,8,-5)
Graph of a Quartic Function with zeros at (-6,4,8,-2)
Graph of a Quartic Function with zeros at (-6,4,8,1)
Graph of a Quartic Function with zeros at (-6,4,8,4)
Graph of a Quartic Function with zeros at (-6,4,15,-5)
Graph of a Quartic Function with zeros at (-6,4,15,-2)
Graph of a Quartic Function with zeros at (-6,4,15,1)
Graph of a Quartic Function with zeros at (-6,4,15,4)
Graph of a Quartic Function with zeros at (-6,12,-20,-5)
Graph of a Quartic Function with zeros at (-6,12,-20,-2)
Graph of a Quartic Function with zeros at (-6,12,-20,1)
Graph of a Quartic Function with zeros at (-6,12,-20,4)
Graph of a Quartic Function with zeros at (-6,12,-13,-5)
Graph of a Quartic Function with zeros at (-6,12,-13,-2)
Graph of a Quartic Function with zeros at (-6,12,-13,1)
Graph of a Quartic Function with zeros at (-6,12,-13,4)
Graph of a Quartic Function with zeros at (-6,12,-6,-5)
Graph of a Quartic Function with zeros at (-6,12,-6,-2)
Graph of a Quartic Function with zeros at (-6,12,-6,1)
Graph of a Quartic Function with zeros at (-6,12,-6,4)
Graph of a Quartic Function with zeros at (-6,12,1,-5)
Graph of a Quartic Function with zeros at (-6,12,1,-2)
Graph of a Quartic Function with zeros at (-6,12,1,1)
Graph of a Quartic Function with zeros at (-6,12,1,4)
Graph of a Quartic Function with zeros at (-6,12,8,-5)
Graph of a Quartic Function with zeros at (-6,12,8,-2)
Graph of a Quartic Function with zeros at (-6,12,8,1)
Graph of a Quartic Function with zeros at (-6,12,8,4)
Graph of a Quartic Function with zeros at (-6,12,15,-5)
Graph of a Quartic Function with zeros at (-6,12,15,-2)
Graph of a Quartic Function with zeros at (-6,12,15,1)
Graph of a Quartic Function with zeros at (-6,12,15,4)
Graph of a Quartic Function with zeros at (3,-20,-20,-5)
Graph of a Quartic Function with zeros at (3,-20,-20,-2)
Graph of a Quartic Function with zeros at (3,-20,-20,1)
Graph of a Quartic Function with zeros at (3,-20,-20,4)
Graph of a Quartic Function with zeros at (3,-20,-13,-5)
Graph of a Quartic Function with zeros at (3,-20,-13,-2)
Graph of a Quartic Function with zeros at (3,-20,-13,1)
Graph of a Quartic Function with zeros at (3,-20,-13,4)
Graph of a Quartic Function with zeros at (3,-20,-6,-5)
Graph of a Quartic Function with zeros at (3,-20,-6,-2)
Graph of a Quartic Function with zeros at (3,-20,-6,1)
Graph of a Quartic Function with zeros at (3,-20,-6,4)
Graph of a Quartic Function with zeros at (3,-20,1,-5)
Graph of a Quartic Function with zeros at (3,-20,1,-2)
Graph of a Quartic Function with zeros at (3,-20,1,1)
Graph of a Quartic Function with zeros at (3,-20,1,4)
Graph of a Quartic Function with zeros at (3,-20,8,-5)
Graph of a Quartic Function with zeros at (3,-20,8,-2)
Graph of a Quartic Function with zeros at (3,-20,8,1)
Graph of a Quartic Function with zeros at (3,-20,8,4)
Graph of a Quartic Function with zeros at (3,-20,15,-5)
Graph of a Quartic Function with zeros at (3,-20,15,-2)
Graph of a Quartic Function with zeros at (3,-20,15,1)
Graph of a Quartic Function with zeros at (3,-20,15,4)
Graph of a Quartic Function with zeros at (3,-12,-20,-5)
Graph of a Quartic Function with zeros at (3,-12,-20,-2)
Graph of a Quartic Function with zeros at (3,-12,-20,1)
Graph of a Quartic Function with zeros at (3,-12,-20,4)
Graph of a Quartic Function with zeros at (3,-12,-13,-5)
Graph of a Quartic Function with zeros at (3,-12,-13,-2)
Graph of a Quartic Function with zeros at (3,-12,-13,1)
Graph of a Quartic Function with zeros at (3,-12,-13,4)
Graph of a Quartic Function with zeros at (3,-12,-6,-5)
Graph of a Quartic Function with zeros at (3,-12,-6,-2)
Graph of a Quartic Function with zeros at (3,-12,-6,1)
Graph of a Quartic Function with zeros at (3,-12,-6,4)
Graph of a Quartic Function with zeros at (3,-12,1,-5)
Graph of a Quartic Function with zeros at (3,-12,1,-2)
Graph of a Quartic Function with zeros at (3,-12,1,1)
Graph of a Quartic Function with zeros at (3,-12,1,4)
Graph of a Quartic Function with zeros at (3,-12,8,-5)
Graph of a Quartic Function with zeros at (3,-12,8,-2)
Graph of a Quartic Function with zeros at (3,-12,8,1)
Graph of a Quartic Function with zeros at (3,-12,8,4)
Graph of a Quartic Function with zeros at (3,-12,15,-5)
Graph of a Quartic Function with zeros at (3,-12,15,-2)
Graph of a Quartic Function with zeros at (3,-12,15,1)
Graph of a Quartic Function with zeros at (3,-12,15,4)
Graph of a Quartic Function with zeros at (3,-4,-20,-5)
Graph of a Quartic Function with zeros at (3,-4,-20,-2)
Graph of a Quartic Function with zeros at (3,-4,-20,1)
Graph of a Quartic Function with zeros at (3,-4,-20,4)
Graph of a Quartic Function with zeros at (3,-4,-13,-5)
Graph of a Quartic Function with zeros at (3,-4,-13,-2)
Graph of a Quartic Function with zeros at (3,-4,-13,1)
Graph of a Quartic Function with zeros at (3,-4,-13,4)
Graph of a Quartic Function with zeros at (3,-4,-6,-5)
Graph of a Quartic Function with zeros at (3,-4,-6,-2)
Graph of a Quartic Function with zeros at (3,-4,-6,1)
Graph of a Quartic Function with zeros at (3,-4,-6,4)
Graph of a Quartic Function with zeros at (3,-4,1,-5)
Graph of a Quartic Function with zeros at (3,-4,1,-2)
Graph of a Quartic Function with zeros at (3,-4,1,1)
Graph of a Quartic Function with zeros at (3,-4,1,4)
Graph of a Quartic Function with zeros at (3,-4,8,-5)
Graph of a Quartic Function with zeros at (3,-4,8,-2)
Graph of a Quartic Function with zeros at (3,-4,8,1)
Graph of a Quartic Function with zeros at (3,-4,8,4)
Graph of a Quartic Function with zeros at (3,-4,15,-5)
Graph of a Quartic Function with zeros at (3,-4,15,-2)
Graph of a Quartic Function with zeros at (3,-4,15,1)
Graph of a Quartic Function with zeros at (3,-4,15,4)
Graph of a Quartic Function with zeros at (3,4,-20,-5)
Graph of a Quartic Function with zeros at (3,4,-20,-2)
Graph of a Quartic Function with zeros at (3,4,-20,1)
Graph of a Quartic Function with zeros at (3,4,-20,4)
Graph of a Quartic Function with zeros at (3,4,-13,-5)
Graph of a Quartic Function with zeros at (3,4,-13,-2)
Graph of a Quartic Function with zeros at (3,4,-13,1)
Graph of a Quartic Function with zeros at (3,4,-13,4)
Graph of a Quartic Function with zeros at (3,4,-6,-5)
Graph of a Quartic Function with zeros at (3,4,-6,-2)
Graph of a Quartic Function with zeros at (3,4,-6,1)
Graph of a Quartic Function with zeros at (3,4,-6,4)
Graph of a Quartic Function with zeros at (3,4,1,-5)
Graph of a Quartic Function with zeros at (3,4,1,-2)
Graph of a Quartic Function with zeros at (3,4,1,1)
Graph of a Quartic Function with zeros at (3,4,1,4)
Graph of a Quartic Function with zeros at (3,4,8,-5)
Graph of a Quartic Function with zeros at (3,4,8,-2)
Graph of a Quartic Function with zeros at (3,4,8,1)
Graph of a Quartic Function with zeros at (3,4,8,4)
Graph of a Quartic Function with zeros at (3,4,15,-5)
Graph of a Quartic Function with zeros at (3,4,15,-2)
Graph of a Quartic Function with zeros at (3,4,15,1)
Graph of a Quartic Function with zeros at (3,4,15,4)
Graph of a Quartic Function with zeros at (3,12,-20,-5)
Graph of a Quartic Function with zeros at (3,12,-20,-2)
Graph of a Quartic Function with zeros at (3,12,-20,1)
Graph of a Quartic Function with zeros at (3,12,-20,4)
Graph of a Quartic Function with zeros at (3,12,-13,-5)
Graph of a Quartic Function with zeros at (3,12,-13,-2)
Graph of a Quartic Function with zeros at (3,12,-13,1)
Graph of a Quartic Function with zeros at (3,12,-13,4)
Graph of a Quartic Function with zeros at (3,12,-6,-5)
Graph of a Quartic Function with zeros at (3,12,-6,-2)
Graph of a Quartic Function with zeros at (3,12,-6,1)
Graph of a Quartic Function with zeros at (3,12,-6,4)
Graph of a Quartic Function with zeros at (3,12,1,-5)
Graph of a Quartic Function with zeros at (3,12,1,-2)
Graph of a Quartic Function with zeros at (3,12,1,1)
Graph of a Quartic Function with zeros at (3,12,1,4)
Graph of a Quartic Function with zeros at (3,12,8,-5)
Graph of a Quartic Function with zeros at (3,12,8,-2)
Graph of a Quartic Function with zeros at (3,12,8,1)
Graph of a Quartic Function with zeros at (3,12,8,4)
Graph of a Quartic Function with zeros at (3,12,15,-5)
Graph of a Quartic Function with zeros at (3,12,15,-2)
Graph of a Quartic Function with zeros at (3,12,15,1)
Graph of a Quartic Function with zeros at (3,12,15,4)
Graph of a Quartic Function with zeros at (12,-20,-20,-5)
Graph of a Quartic Function with zeros at (12,-20,-20,-2)
Graph of a Quartic Function with zeros at (12,-20,-20,1)
Graph of a Quartic Function with zeros at (12,-20,-20,4)
Graph of a Quartic Function with zeros at (12,-20,-13,-5)
Graph of a Quartic Function with zeros at (12,-20,-13,-2)
Graph of a Quartic Function with zeros at (12,-20,-13,1)
Graph of a Quartic Function with zeros at (12,-20,-13,4)
Graph of a Quartic Function with zeros at (12,-20,-6,-5)
Graph of a Quartic Function with zeros at (12,-20,-6,-2)
Graph of a Quartic Function with zeros at (12,-20,-6,1)
Graph of a Quartic Function with zeros at (12,-20,-6,4)
Graph of a Quartic Function with zeros at (12,-20,1,-5)
Graph of a Quartic Function with zeros at (12,-20,1,-2)
Graph of a Quartic Function with zeros at (12,-20,1,1)
Graph of a Quartic Function with zeros at (12,-20,1,4)
Graph of a Quartic Function with zeros at (12,-20,8,-5)
Graph of a Quartic Function with zeros at (12,-20,8,-2)
Graph of a Quartic Function with zeros at (12,-20,8,1)
Graph of a Quartic Function with zeros at (12,-20,8,4)
Graph of a Quartic Function with zeros at (12,-20,15,-5)
Graph of a Quartic Function with zeros at (12,-20,15,-2)
Graph of a Quartic Function with zeros at (12,-20,15,1)
Graph of a Quartic Function with zeros at (12,-20,15,4)
Graph of a Quartic Function with zeros at (12,-12,-20,-5)
Graph of a Quartic Function with zeros at (12,-12,-20,-2)
Graph of a Quartic Function with zeros at (12,-12,-20,1)
Graph of a Quartic Function with zeros at (12,-12,-20,4)
Graph of a Quartic Function with zeros at (12,-12,-13,-5)
Graph of a Quartic Function with zeros at (12,-12,-13,-2)
Graph of a Quartic Function with zeros at (12,-12,-13,1)
Graph of a Quartic Function with zeros at (12,-12,-13,4)
Graph of a Quartic Function with zeros at (12,-12,-6,-5)
Graph of a Quartic Function with zeros at (12,-12,-6,-2)
Graph of a Quartic Function with zeros at (12,-12,-6,1)
Graph of a Quartic Function with zeros at (12,-12,-6,4)
Graph of a Quartic Function with zeros at (12,-12,1,-5)
Graph of a Quartic Function with zeros at (12,-12,1,-2)
Graph of a Quartic Function with zeros at (12,-12,1,1)
Graph of a Quartic Function with zeros at (12,-12,1,4)
Graph of a Quartic Function with zeros at (12,-12,8,-5)
Graph of a Quartic Function with zeros at (12,-12,8,-2)
Graph of a Quartic Function with zeros at (12,-12,8,1)
Graph of a Quartic Function with zeros at (12,-12,8,4)
Graph of a Quartic Function with zeros at (12,-12,15,-5)
Graph of a Quartic Function with zeros at (12,-12,15,-2)
Graph of a Quartic Function with zeros at (12,-12,15,1)
Graph of a Quartic Function with zeros at (12,-12,15,4)
Graph of a Quartic Function with zeros at (12,-4,-20,-5)
Graph of a Quartic Function with zeros at (12,-4,-20,-2)
Graph of a Quartic Function with zeros at (12,-4,-20,1)
Graph of a Quartic Function with zeros at (12,-4,-20,4)
Graph of a Quartic Function with zeros at (12,-4,-13,-5)
Graph of a Quartic Function with zeros at (12,-4,-13,-2)
Graph of a Quartic Function with zeros at (12,-4,-13,1)
Graph of a Quartic Function with zeros at (12,-4,-13,4)
Graph of a Quartic Function with zeros at (12,-4,-6,-5)
Graph of a Quartic Function with zeros at (12,-4,-6,-2)
Graph of a Quartic Function with zeros at (12,-4,-6,1)
Graph of a Quartic Function with zeros at (12,-4,-6,4)
Graph of a Quartic Function with zeros at (12,-4,1,-5)
Graph of a Quartic Function with zeros at (12,-4,1,-2)
Graph of a Quartic Function with zeros at (12,-4,1,1)
Graph of a Quartic Function with zeros at (12,-4,1,4)
Graph of a Quartic Function with zeros at (12,-4,8,-5)
Graph of a Quartic Function with zeros at (12,-4,8,-2)
Graph of a Quartic Function with zeros at (12,-4,8,1)
Graph of a Quartic Function with zeros at (12,-4,8,4)
Graph of a Quartic Function with zeros at (12,-4,15,-5)
Graph of a Quartic Function with zeros at (12,-4,15,-2)
Graph of a Quartic Function with zeros at (12,-4,15,1)
Graph of a Quartic Function with zeros at (12,-4,15,4)
Graph of a Quartic Function with zeros at (12,4,-20,-5)
Graph of a Quartic Function with zeros at (12,4,-20,-2)
Graph of a Quartic Function with zeros at (12,4,-20,1)
Graph of a Quartic Function with zeros at (12,4,-20,4)
Graph of a Quartic Function with zeros at (12,4,-13,-5)
Graph of a Quartic Function with zeros at (12,4,-13,-2)
Graph of a Quartic Function with zeros at (12,4,-13,1)
Graph of a Quartic Function with zeros at (12,4,-13,4)
Graph of a Quartic Function with zeros at (12,4,-6,-5)
Graph of a Quartic Function with zeros at (12,4,-6,-2)
Graph of a Quartic Function with zeros at (12,4,-6,1)
Graph of a Quartic Function with zeros at (12,4,-6,4)
Graph of a Quartic Function with zeros at (12,4,1,-5)
Graph of a Quartic Function with zeros at (12,4,1,-2)
Graph of a Quartic Function with zeros at (12,4,1,1)
Graph of a Quartic Function with zeros at (12,4,1,4)
Graph of a Quartic Function with zeros at (12,4,8,-5)
Graph of a Quartic Function with zeros at (12,4,8,-2)
Graph of a Quartic Function with zeros at (12,4,8,1)
Graph of a Quartic Function with zeros at (12,4,8,4)
Graph of a Quartic Function with zeros at (12,4,15,-5)
Graph of a Quartic Function with zeros at (12,4,15,-2)
Graph of a Quartic Function with zeros at (12,4,15,1)
Graph of a Quartic Function with zeros at (12,4,15,4)
Graph of a Quartic Function with zeros at (12,12,-20,-5)
Graph of a Quartic Function with zeros at (12,12,-20,-2)
Graph of a Quartic Function with zeros at (12,12,-20,1)
Graph of a Quartic Function with zeros at (12,12,-20,4)
Graph of a Quartic Function with zeros at (12,12,-13,-5)
Graph of a Quartic Function with zeros at (12,12,-13,-2)
Graph of a Quartic Function with zeros at (12,12,-13,1)
Graph of a Quartic Function with zeros at (12,12,-13,4)
Graph of a Quartic Function with zeros at (12,12,-6,-5)
Graph of a Quartic Function with zeros at (12,12,-6,-2)
Graph of a Quartic Function with zeros at (12,12,-6,1)
Graph of a Quartic Function with zeros at (12,12,-6,4)
Graph of a Quartic Function with zeros at (12,12,1,-5)
Graph of a Quartic Function with zeros at (12,12,1,-2)
Graph of a Quartic Function with zeros at (12,12,1,1)
Graph of a Quartic Function with zeros at (12,12,1,4)
Graph of a Quartic Function with zeros at (12,12,8,-5)
Graph of a Quartic Function with zeros at (12,12,8,-2)
Graph of a Quartic Function with zeros at (12,12,8,1)
Graph of a Quartic Function with zeros at (12,12,8,4)
Graph of a Quartic Function with zeros at (12,12,15,-5)
Graph of a Quartic Function with zeros at (12,12,15,-2)
Graph of a Quartic Function with zeros at (12,12,15,1)
Graph of a Quartic Function with zeros at (12,12,15,4)
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