Write down the general form of the function of a parabola as
F(x) = ax^2 + bx + c
where x is the dependent variable, a is the coefficient of the second degree term, b is the coefficient of the first degree term and c is a constant.
Write down a parabola function that agrees with the general form of the parabola function. Use a = 2, b = 3 and c= 5 for the coefficients in the parabolic function for this example to obtain
F(x) = 2x^2 + 3x + 5
Substitute a negative value of -1 in the function to obtain
F(x) = 2(-1)^2 + 3(-1) + 5
Simplify to obtain
F(x) = 2 + -3 + 5
and compute that
F(x) - 4 for x= -1
Conclude that x = -1 is in the domain of the parabola, since a real number for F(x) is obtained when -1 is substituted for x in the equation.
Substitute a value of x = 0 and a value of x = 1, in the same manner as in the previous step, to verify that 0 and 1 are also in the domain, since they will result in a real number for F(x).
Conclude that any real number used for x will result in a real number for F(x), since the function F(x) does not include a term where x is in the denominator (which would result in division by zero for x = 0). Also conclude that for any parabola of the general form
F(x) = ax^2 + bx + c
that the domain of the parabola is all real numbers, since the general form does not include a term where x is in the denominator.