Question

2x² - 8x + 6. 1. Дана функция у = 2х² А) Найдите координаты вершины парабо Б) Найдите точки пересечения с осями кс В) Найдите ось симметрии параболы. Г) Постройте график функции.​

Answer 1

Ответ:

график представляет собой параболу. График можно задать по точкам х;у подставляя произвольное значение х, определяем чему равен у. Или используя свойства параболы определяем точки пересечения с осями координат, находим координаты вершины параболы.

Answer 2

Function Analysis: y = 2x² - 8x + 6

To analyze the given function, let's go through each question step by step.

A) Finding the Vertex: The vertex of a parabola can be found using the formula: x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, the quadratic equation is y = 2x² - 8x + 6. Comparing it to the standard form of a quadratic equation (y = ax² + bx + c), we can see that a = 2, b = -8, and c = 6.

Using the formula, we can find the x-coordinate of the vertex: x = -(-8) / (2 * 2) = 8 / 4 = 2.

To find the y-coordinate of the vertex, substitute the x-coordinate back into the equation: y = 2(2)² - 8(2) + 6 = 2(4) - 16 + 6 = 8 - 16 + 6 = -2.

Therefore, the coordinates of the vertex are (2, -2).

B) Finding the x-intercepts (points of intersection with the x-axis): To find the x-intercepts, we set y = 0 and solve for x.

Setting y = 0 in the equation 2x² - 8x + 6 = 0, we get a quadratic equation: 2x² - 8x + 6 = 0.

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Plugging in the values a = 2, b = -8, and c = 6, we get: x = (-(-8) ± √((-8)² - 4 * 2 * 6)) / (2 * 2) = (8 ± √(64 - 48)) / 4 = (8 ± √16) / 4 = (8 ± 4) / 4.

This gives us two possible solutions for x: x₁ = (8 + 4) / 4 = 12 / 4 = 3, x₂ = (8 - 4) / 4 = 4 / 4 = 1.

Therefore, the points of intersection with the x-axis are (3, 0) and (1, 0).

C) Finding the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. Its equation can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, the quadratic equation is y = 2x² - 8x + 6. Comparing it to the standard form of a quadratic equation (y = ax² + bx + c), we can see that a = 2 and b = -8.

Using the formula, we can find the equation of the axis of symmetry: x = -(-8) / (2 * 2) = 8 / 4 = 2.

Therefore, the equation of the axis of symmetry is x = 2.

D) Graphing the function: To graph the function y = 2x² - 8x + 6, we can start by plotting the vertex and the x-intercepts we found earlier.

The vertex is located at (2, -2), and the x-intercepts are at (3, 0) and (1, 0).

Next, we can find a few more points by substituting some x-values into the equation and calculating the corresponding y-values. For example, when x = 0, y = 2(0)² - 8(0) + 6 = 6. So we have the point (0, 6).

Plotting these points on a graph and connecting them with a smooth curve will give us the graph of the function y = 2x² - 8x + 6.


Please note that the graph is a rough approximation and may not be perfectly accurate.

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