Question

Пожалуйста возьмите из интернета какую-нибудь картинку из парабол и составьте к ней уравнения. Прошу помогите!!!!!!!!!!!

Answer 1

В общем парабола записывается как х в квадрате а если ты хочешь ее перенести в прраво или в лево вдоль оси 0х ты должна писать х в кадрате + или минус , а если в доль оси 0у ты должна сделать аналогичное действие что и с 0х

Answer 2

Parabola and its Equation

A parabola is a U-shaped curve that is symmetric about a vertical line called the axis of symmetry. It is defined by a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants.

To better understand the equation of a parabola, let's consider an example and visualize it with a graph.

Let's say we have a parabola with the following characteristics: - Vertex: (2, 3) - Axis of symmetry: x = 2 - Focus: (2, 4) - Directrix: y = 2

To find the equation of this parabola, we can use the vertex form of the equation: y = a(x - h)^2 + k, where (h, k) represents the vertex.

Substituting the given vertex coordinates into the equation, we have: y = a(x - 2)^2 + 3

To determine the value of a, we can use the relationship between the focus and the directrix. For a parabola, the distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.

In this case, the distance from the vertex (2, 3) to the focus (2, 4) is 1, and the distance from the vertex to the directrix y = 2 is also 1. Therefore, we can conclude that a = 1/(4p), where p is the distance from the vertex to the focus or the vertex to the directrix.

Since the distance from the vertex to the focus is 1, we have p = 1. Substituting this value into the equation, we get a = 1/(4 * 1) = 1/4.

Now we can rewrite the equation of the parabola with the value of a: y = (1/4)(x - 2)^2 + 3

This equation represents the parabola with the given characteristics.

Please note that the example above is just one specific case, and the equation of a parabola can vary depending on its characteristics. The general form of the equation is y = ax^2 + bx + c, where a, b, and c can take different values.

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