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Polynomial function (n≤2)

A polynomial function of degree 2 is also called a quadratic function. Its graph is a parabola whose axis of symmetry is parallel to the y-axis.

A quadratic function can be expressed in three formats: 

  • Its general expression f(x) = a.x2 + b.x + c, is known as the "standard" form. a, b and c are the parameters of the function where c caracterizes the height of the parabola (where it intercepts the y-axis). f (0) = c.
  • The "factored" form f(x) = a.(x - z1).(x - z2) reveals the "zeros" of the parabola (i.e. z1 and z2 are the two points where f(z1) = f(z2) = 0) 
  • f(x) = a.(x - h)2 + k  is the "vertex" form. x = h is where on the x-axis the parabola changes direction. x = h is the axis of symmetry. h is the horizontal shift and k the vertical shift of the parabola. This is why the point (h,k) is called the "turning point".  

 This animation helps to understand the influence of each parameter on the form and plot of the function.

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