Question

Построить график функции -x^2+2x

Answer 1

Кароче парабола, смотри фото.........

Answer 2

Graph of the Function -x^2 + 2x

To graph the function -x^2 + 2x, we can start by finding the x-intercepts, y-intercept, and vertex of the parabola represented by the function.

1. X-intercepts: To find the x-intercepts, we set the function equal to zero and solve for x: -x^2 + 2x = 0

Factoring out an x, we get: x(-x + 2) = 0

Setting each factor equal to zero, we find two possible solutions: - x = 0 - -x + 2 = 0, which gives x = 2

Therefore, the x-intercepts are x = 0 and x = 2.

2. Y-intercept: To find the y-intercept, we substitute x = 0 into the function: -0^2 + 2(0) = 0

Therefore, the y-intercept is y = 0.

3. Vertex: The vertex of a parabola can be found using the formula x = -b/2a. In this case, a = -1 and b = 2. x = -2/(2*(-1)) = -2/(-2) = 1

To find the corresponding y-coordinate, we substitute x = 1 into the function: -1^2 + 2(1) = -1 + 2 = 1

Therefore, the vertex is (1, 1).

Now, let's plot these points and sketch the graph of the function -x^2 + 2x:

- X-intercepts: (0, 0) and (2, 0) - Y-intercept: (0, 0) - Vertex: (1, 1)


The graph of the function -x^2 + 2x is a downward-opening parabola that passes through the points (0, 0), (2, 0), and has a vertex at (1, 1).