How to Find the Domain of F for a Parabola

Domain problems, such as the domain parabola problems, are often seen on Algebra II and Calculus tests. As far as math problems go, they are one of the easier problems to solve, as long as you understand the definition of a domain. The domain of a function is defined as the set of all values of x, the independent variable, that result in a real number for F(x), the dependent variable, when x is substituted into the function. A real number is any number except negative or positive infinity or an undefined number, obtained when you divide a number by 0.

Instructions

    • 1

      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.

    • 2

      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

    • 3

      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.

    • 4

      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).

    • 5

      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.

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