Question

Постройте график функции y=x2-2x-3

Answer 1

График функции построен на изображении

Answer 2

Graph of the Function y = x^2 - 2x - 3

To plot the graph of the function y = x^2 - 2x - 3, we can start by finding the x-intercepts, y-intercept, and vertex of the parabola.

1. X-intercepts: To find the x-intercepts, we set y = 0 and solve for x. In this case, we need to solve the equation x^2 - 2x - 3 = 0. We can use the quadratic formula or factorization to find the solutions. The solutions are x = -1 and x = 3.

2. Y-intercept: To find the y-intercept, we set x = 0 and solve for y. Plugging x = 0 into the equation y = x^2 - 2x - 3, we get y = -3.

3. Vertex: The vertex of a parabola in the form y = ax^2 + bx + c can be found using the formula x = -b / (2a). In this case, a = 1, b = -2, and c = -3. Plugging these values into the formula, we get x = 1. Substituting x = 1 into the equation, we find y = -4.

Now, let's plot the graph:


The graph of the function y = x^2 - 2x - 3 is a downward-opening parabola. It intersects the x-axis at x = -1 and x = 3, and the y-axis at y = -3. The vertex of the parabola is located at (1, -4).

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