what point is symmetrical to (-1,-3) for the graph of y = x^2 + 12x + 8
To find the point that is symmetrical to (-1, -3) for the graph of y = x^2 + 12x + 8, we can use the concept of symmetry in a parabola.
The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) represents the vertex. In this case, the given equation y = x^2 + 12x + 8 is already in vertex form, indicating that the vertex is (-6, -20).
Since the parabola is symmetric about the vertex, the point that is symmetrical to (-1, -3) will also have the same x-coordinate as the vertex, but a different y-coordinate.
The x-coordinate of the vertex is -6, so the x-coordinate of the symmetrical point will also be -6.
To find the y-coordinate of the symmetrical point, we need to substitute x = -6 into the equation y = x^2 + 12x + 8:
y = (-6)^2 + 12(-6) + 8
= 36 - 72 + 8
= -28
Therefore, the point that is symmetrical to (-1, -3) on the graph of y = x^2 + 12x + 8 is (-6, -28).