Question

Построить график функций y=x^2-8x+12

Answer 1

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Answer 2

Graph of the Function y = x^2 - 8x + 12

To graph the function y = x^2 - 8x + 12, we can analyze the equation and plot the corresponding points on a coordinate plane.

The general form of the equation is y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = -8, and c = 12.

To find the vertex of the parabola, we can use the formula x = -b/2a. Plugging in the values, we get x = -(-8)/(2*1) = 4. Substituting this value back into the equation, we find y = 4^2 - 8*4 + 12 = 4.

Therefore, the vertex of the parabola is at the point (4, 4).

To find additional points to plot on the graph, we can choose values for x and calculate the corresponding y values. Let's choose a few values for x:

- When x = 0, y = 0^2 - 8*0 + 12 = 12. So we have the point (0, 12). - When x = 1, y = 1^2 - 8*1 + 12 = 5. So we have the point (1, 5). - When x = 2, y = 2^2 - 8*2 + 12 = 4. So we have the point (2, 4). - When x = 3, y = 3^2 - 8*3 + 12 = 3. So we have the point (3, 3). - When x = 5, y = 5^2 - 8*5 + 12 = -3. So we have the point (5, -3).

Now, let's plot these points on a graph:


The graph of the function y = x^2 - 8x + 12 is a downward-opening parabola with its vertex at (4, 4). The parabola intersects the x-axis at x = 0, 6, and the y-axis at y = 12.