Here, a = 1 (the coefficient of x²) and b = 4 (the coefficient of x). Plugging these values into the formula, we get:
x = -4 / (2 * 1) = -4 / 2 = -2.
Now that we have the x-coordinate of the vertex, we need to find the corresponding y-coordinate by substituting x = -2 back into the original equation:
y = (-2)² + 4(-2) + 6.
Calculating this gives us:
y = 4 – 8 + 6 = 2.
So, the vertex of the parabola is at the point (-2, 2). This point represents the minimum or maximum of the parabola, depending on the direction it opens. Since the coefficient of x² is positive, the parabola opens upwards, and therefore, the vertex is a minimum point.