Question

Дам 40 баллов.. Пожалуйста помогите. Постройте полное исследование функции и постройте её график.у=6-7х-х^2​

Answer 1

Ответ:

Масштаб (от немецкого Stab – палка) – это отношение длины отрезка на карте, плане, аэро- или космическом снимке к его действительной длине на местности.

Рассмотрим виды масштабов.

Численный масштаб

Это масштаб, выраженный в виде дроби, где числитель – единица, а знаменатель – число, показывающее во сколько раз уменьшено изображение.

Пошаговое объяснение:

Вот

Answer 2

Function Analysis and Graph Plotting: y = 6 - 7x - x^2

To analyze the function y = 6 - 7x - x^2 and plot its graph, we will go through the following steps:

1. Determine the domain and range of the function. 2. Find the x-intercepts (zeros) and y-intercept of the function. 3. Determine the vertex of the parabola. 4. Find the axis of symmetry. 5. Plot the graph of the function.

Let's go through each step in detail.

Step 1: Determine the Domain and Range

The domain of a function represents all the possible input values (x-values) for which the function is defined. In this case, since we have a polynomial function, the domain is all real numbers (-∞, +∞).

The range of a function represents all the possible output values (y-values) that the function can take. For this quadratic function, the range is determined by the vertex. Since the coefficient of the x^2 term is negative, the parabola opens downwards, and the range is (-∞, y-coordinate of the vertex].

Step 2: Find the x-intercepts and y-intercept

To find the x-intercepts (zeros) of the function, we set y = 0 and solve for x. In this case, we need to solve the quadratic equation:

- x^2 - 7x + 6 = 0

Factoring the equation, we get:

- (x - 6)(x - 1) = 0

Setting each factor equal to zero, we find the x-intercepts:

- x - 6 = 0 => x = 6 - x - 1 = 0 => x = 1

So, the x-intercepts are x = 6 and x = 1.

To find the y-intercept, we set x = 0 and solve for y:

- y = 6 - 7(0) - (0)^2 - y = 6

So, the y-intercept is y = 6.

Step 3: Determine the Vertex

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

- x = -b / (2a) - y = f(x)

In this case, a = -1, b = -7, and c = 6. Substituting these values into the formula, we get:

- x = -(-7) / (2 * -1) = 7 / -2 = -3.5 - y = 6 - 7(-3.5) - (-3.5)^2 = 6 + 24.5 - 12.25 = 18.25

So, the vertex of the parabola is (-3.5, 18.25).

Step 4: Find the Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex of the parabola. The equation of the axis of symmetry can be found using the formula:

- x = -b / (2a)

In this case, substituting the values of a and b, we get:

- x = -(-7) / (2 * -1) = 7 / -2 = -3.5

So, the axis of symmetry is x = -3.5.

Step 5: Plot the Graph

Now that we have all the necessary information, we can plot the graph of the function y = 6 - 7x - x^2.

The graph will be a downward-opening parabola with the vertex at (-3.5, 18.25). The x-intercepts are at x = 6 and x = 1, and the y-intercept is at y = 6. The axis of symmetry is x = -3.5.

Here is the graph of the function:


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