The area between the vertex of the parabola and x-axis

1-) Warning

If you don't know about the following topics, you will have problems in this kata.

• Quadratic equations
• Parabola
• Integral

2-) Explanation

• I will give you 3 values as input in the kata. These are a , b , c. The value of a will never be given as 0. These values are the coefficients of the following equation.

  $f(x)=a{x}^2+bx+cf(x)\; =\; ax^2\; +\; bx\; +\; c$

• The graph of this equation is a parabola.

• This kata asks you for the area between the vertex of the parabola and x-axis.

• Don't forget area isn't negative.

3-) Details

• If the equation hasn't real roots, you should return 0. Because there isn't any area.

• If the equation has 2 equal real roots, you should return 0. Because 0 is the real area.

• If the equation has 2 unequal real root, you should return the real area.

  For example

  The real area: 35.265720  --->  return 35.265720
  

• Given values is definitely between -4000 with 4000. Because the result should be under the DOUBLE_MAX value.

• I set up the tolerance to 10^-6 for the decimal errors.

Letter for you

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-founded by theprotagonist