Question

Квадратичная функция, ее график и свойства. Урок 1 Как можно получить график функции y = 3(x + 5)2 – 8 из графика функции y = 3x2? путем сдвига графика функции y = 3x2 вдоль оси Ox на 5 единиц вправо и вдоль оси Oy на 8 единиц вниз путем сдвига графика функции y = 3x2 вдоль оси Ox на 5 единиц влево и вдоль оси Oy на 8 единиц вниз путем сдвига графика функции y = 3x2 вдоль оси Ox на 5 единиц вправо и вдоль оси Oy на 8 единиц вверх путем сдвига графика функции y = 3x2 вдоль оси Ox на 5 единиц влево и вдоль оси Oy на 8 единиц вверхпожалуйста, помогите ​

Answer 1

ответ на фото и объяснения там же

Answer 2

Quadratic Function, Graph, and Properties

A quadratic function is a polynomial function of degree 2, which means its highest power of the variable is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

The graph of a quadratic function is a parabola. The shape of the parabola depends on the value of the coefficient a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward.

The vertex of the parabola is the point where it reaches its minimum or maximum value. The vertex can be found using the formula x = -b / (2a). The y-coordinate of the vertex can be obtained by substituting the x-coordinate into the quadratic function.

Other important properties of quadratic functions include the axis of symmetry, which is a vertical line passing through the vertex, and the y-intercept, which is the point where the parabola intersects the y-axis.

Obtaining the Graph of y = 3(x + 5)^2 - 8 from the Graph of y = 3x^2

To obtain the graph of the function y = 3(x + 5)^2 - 8 from the graph of y = 3x^2, we need to perform certain transformations on the original graph.

1. Horizontal Shift: To shift the graph of y = 3x^2 5 units to the right, we need to replace x with (x - 5) in the equation. This will shift the graph horizontally to the right by 5 units.

The equation becomes y = 3(x - 5 + 5)^2 - 8.

2. Vertical Shift: To shift the graph of y = 3(x - 5)^2 - 8 8 units downward, we need to subtract 8 from the equation. This will shift the graph vertically downward by 8 units.

The equation becomes y = 3(x - 5)^2 - 8 - 8.

By performing these transformations, we obtain the equation y = 3(x + 5)^2 - 16, which represents the graph of y = 3(x + 5)^2 - 8 obtained from the graph of y = 3x^2.

Please note that the transformations mentioned above are applied in the order specified. First, the horizontal shift is performed, and then the vertical shift is applied.

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