Question

Задайте функцию y=x^2-6x+5 на множество действительны чисел графическим способом.

Answer 1

Вершина параболы
x₀=-b/2a=-(-6)/2=6/2=3
y₀=9-18+5=-4

x₁=0  y₁=5
x₂=6  y₂=36-36+5=0

Answer 2

Graphical Representation of the Function y = x^2 - 6x + 5

To graph the function y = x^2 - 6x + 5 on the set of real numbers, we can follow these steps:

1. Identify the Vertex: The vertex of the parabola represented by the function y = ax^2 + bx + c can be found using the formula x = -b/2a. In this case, for the given function y = x^2 - 6x + 5, the x-coordinate of the vertex can be found using x = -(-6)/(2*1).

2. Plot the Vertex: Once the x-coordinate of the vertex is found, we can substitute it back into the original function to find the y-coordinate of the vertex. This gives us the coordinates of the vertex, which we can plot on the graph.

3. Find the y-intercept: The y-intercept occurs when x = 0. Substituting x = 0 into the function gives us the y-intercept.

4. Find the x-intercepts (if any): The x-intercepts occur when y = 0. We can solve the quadratic equation x^2 - 6x + 5 = 0 to find the x-intercepts.

5. Plot Additional Points: We can choose additional x-values to find the corresponding y-values and plot these points on the graph.

6. Draw the Parabola: Using the plotted points, we can draw the parabola that represents the function.

Let's proceed with these steps to graph the function.

Steps to Graph the Function y = x^2 - 6x + 5

1. Identify the Vertex: - Using the formula x = -b/2a, we find the x-coordinate of the vertex: - x = -(-6)/(2*1) = 3 - Therefore, the x-coordinate of the vertex is 3.

2. Plot the Vertex: - Substituting x = 3 into the function gives us the y-coordinate of the vertex: - y = 3^2 - 6*3 + 5 = 9 - 18 + 5 = -4 - Therefore, the vertex is at the point (3, -4).

3. Find the y-intercept: - When x = 0, y = 0^2 - 6*0 + 5 = 5 - Therefore, the y-intercept is at the point (0, 5).

4. Find the x-intercepts (if any): - To find the x-intercepts, we solve the quadratic equation x^2 - 6x + 5 = 0. - The solutions are x = 1 and x = 5. - Therefore, the x-intercepts are at the points (1, 0) and (5, 0).

5. Plot Additional Points: - We can choose additional x-values to find the corresponding y-values and plot these points on the graph.

6. Draw the Parabola: - Using the plotted points, we can draw the parabola that represents the function.

Now that we have the necessary points, we can plot the graph of the function y = x^2 - 6x + 5.