Question

Как найти область определения функции у параболы

Answer 1

От минус бесконечности до + бесконечности

Answer 2

Finding the Domain of a Parabola Function

To find the domain of a parabola function, we need to determine the set of all possible input values (x-values) for which the function is defined. The domain of a parabola function depends on the specific equation of the parabola.

Here are the steps to find the domain of a parabola function:

1. Identify the equation of the parabola: The equation of a parabola can be in different forms, such as vertex form, standard form, or intercept form. The specific form of the equation will determine the method used to find the domain.

2. Analyze the equation: Depending on the form of the equation, different considerations need to be taken into account to determine the domain.

- If the equation is in vertex form (y = a(x - h)^2 + k), the domain is all real numbers (-∞, +∞) because the parabola extends infinitely in both directions along the x-axis.

- If the equation is in standard form (y = ax^2 + bx + c), the domain is also all real numbers (-∞, +∞) because the parabola extends infinitely in both directions along the x-axis.

- If the equation is in intercept form (y = a(x - p)(x - q)), where p and q are the x-intercepts, the domain is the set of all real numbers except for the x-values of the intercepts. In other words, the domain is (-∞, p) ∪ (p, q) ∪ (q, +∞).

3. Solve for any restrictions: In some cases, there may be additional restrictions on the domain based on the context of the problem or the specific values of the coefficients in the equation. For example, if the parabola represents a physical situation, there may be limitations on the x-values that make sense in that context.

It's important to note that without a specific equation for the parabola, it is not possible to determine the exact domain. The steps provided above are general guidelines based on common forms of parabola equations.

Example: Let's consider the equation y = x^2 + 8x - 7. To find the domain of this parabola function, we can follow the steps outlined above:

1. Identify the equation: y = x^2 + 8x - 7.

2. Analyze the equation: Since the equation is in standard form, the domain is all real numbers (-∞, +∞) because the parabola extends infinitely in both directions along the x-axis.

Therefore, the domain of the parabola function y = x^2 + 8x - 7 is (-∞, +∞).

I hope this helps! Let me know if you have any further questions.