Question

Y=x^2-4x-5 8 класс график функции

Answer 1

Graph of the Function

To understand the graph of the function Y = x^2 - 4x - 5 + 8, we can analyze the equation and identify key points and characteristics.

The given equation is a quadratic function in the form Y = ax^2 + bx + c, where a = 1, b = -4, and c = -5 + 8 = 3.

The graph of a quadratic function is a parabola. The coefficient a determines whether the parabola opens upwards (if a > 0) or downwards (if a < 0). In this case, since a = 1, the parabola opens upwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a). Substituting the values, we get x = -(-4) / (2 * 1) = 2. Plugging this value back into the equation, we can find the corresponding y-coordinate: Y = (2)^2 - 4(2) - 5 + 8 = -1.

Therefore, the vertex of the parabola is at the point (2, -1).

To determine the shape of the parabola, we can look at the coefficient a. Since a > 0, the parabola opens upwards, forming a "U" shape.

Key Points and Characteristics

- Vertex: The vertex of the parabola is at the point (2, -1). - Axis of Symmetry: The axis of symmetry is a vertical line passing through the vertex. In this case, the equation of the axis of symmetry is x = 2. - Y-Intercept: To find the y-intercept, we can substitute x = 0 into the equation: Y = (0)^2 - 4(0) - 5 + 8 = 3. Therefore, the y-intercept is at the point (0, 3). - X-Intercepts: To find the x-intercepts, we can set Y = 0 and solve for x. The equation becomes x^2 - 4x - 5 + 8 = 0. Factoring or using the quadratic formula, we find that the x-intercepts are approximately x = -1 and x = 5.

Graph of the Function

Based on the information above, the graph of the function Y = x^2 - 4x - 5 + 8 is a parabola that opens upwards. The vertex is at the point (2, -1), and the axis of symmetry is the vertical line x = 2. The y-intercept is at the point (0, 3), and the x-intercepts are approximately x = -1 and x = 5.

Please note that the graph is not provided here, but you can plot the points and sketch the parabola based on the information provided.

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