Question

Изобразить график функции и указать ее свойства y=x^2+6x-4

Answer 1

Graph of the Function y = x^2 + 6x - 4

To graph the function y = x^2 + 6x - 4, we can analyze its properties and plot the corresponding points.

Analyzing the Function

To understand the properties of the function y = x^2 + 6x - 4, we can look at the equation in standard form: y = ax^2 + bx + c. In this case, a = 1, b = 6, and c = -4.

1. Vertex: The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this case, the vertex is (-3, -13).2. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex. For this function, the axis of symmetry is x = -3.3. y-intercept: The y-intercept is the point where the graph intersects the y-axis. To find it, we substitute x = 0 into the equation. In this case, the y-intercept is -4.4. x-intercepts: The x-intercepts are the points where the graph intersects the x-axis. To find them, we set y = 0 and solve for x. In this case, the x-intercepts are approximately -6.77 and 0.77.

Plotting the Graph

Using the information above, we can plot the graph of the function y = x^2 + 6x - 4.

Here is the graph:


The graph is a parabola that opens upwards. The vertex is located at (-3, -13), and the axis of symmetry is the vertical line x = -3. The y-intercept is -4, and the x-intercepts are approximately -6.77 and 0.77.

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