The vertex of a parabola given by the equation in standard form, y = ax^2 + bx + c, can be found using the formula for the x-coordinate of the vertex, which is x = -b/(2a).
In this case, the equation provided is y = x^2 + 12x + 3. Here, a = 1, b = 12, and c = 3.
To find the x-coordinate of the vertex, we can plug in our values into the formula:
x = -b / (2a) = -12 / (2 * 1) = -12 / 2 = -6Now that we have the x-coordinate, we can find the y-coordinate by substituting x = -6 back into the original equation:
y = (-6)^2 + 12(-6) + 3 = 36 - 72 + 3 = -33Thus, the coordinates of the vertex are (-6, -33).
In conclusion, the vertex of the parabola defined by the equation y = x^2 + 12x + 3 is (-6, -33).