Question

Постройте график функции у = 3х в квадрате + 6х+1

Answer 1

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Answer 2

Graph of the Function y = 3x^2 + 6x + 1

To graph the function y = 3x^2 + 6x + 1, we can use the standard form of a quadratic function, which is y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 3, b = 6, and c = 1.

The graph of a quadratic function is a parabola. The vertex of the parabola can be found using the formula x = -b/(2a), and then the y-coordinate of the vertex can be found by substituting this x-value into the original function.

The x-coordinate of the vertex is given by: x = -b / (2a)

Substitute the values of a and b: x = -6 / (2*3) = -1

Now, substitute x = -1 into the original function to find the y-coordinate of the vertex: y = 3*(-1)^2 + 6*(-1) + 1 = 3 - 6 + 1 = -2

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

The parabola opens upwards because the coefficient of x^2 (which is 3) is positive.

Let's plot the vertex and a few additional points to sketch the graph of the function.

Plotting the Graph

Using the vertex and a few additional points, we can sketch the graph of the function y = 3x^2 + 6x + 1.

- Vertex: (-1, -2) - Additional points: - When x = 0, y = 3*0^2 + 6*0 + 1 = 1 - When x = 1, y = 3*1^2 + 6*1 + 1 = 3 + 6 + 1 = 10

Now, let's plot these points and sketch the parabola.

Vertex: (-1, -2)
Additional points:
(0, 1)
(1, 10)

Now, we can sketch the parabola passing through these points.

Conclusion

The graph of the function y = 3x^2 + 6x + 1 is a parabola that opens upwards, and its vertex is located at the point (-1, -2). The parabola passes through the points (0, 1) and (1, 10).