To find the vertex of the quadratic equation y = 3x² + 6x + 4, we can use the vertex formula derived from the standard form of a parabola.
The vertex (h, k) can be found using the formula:
h = -b / (2a)
In our equation, the coefficients are:
- a = 3
- b = 6
- c = 4
Now, substitute the values of a and b into the formula:
h = -6 / (2 * 3) = -6 / 6 = -1
Next, to find the y-coordinate (k) of the vertex, substitute x = -1 back into the original equation:
k = 3(-1)² + 6(-1) + 4
Calculating this gives:
k = 3(1) – 6 + 4 = 3 – 6 + 4 = 1
Thus, the vertex of the parabola represented by the equation y = 3x² + 6x + 4 is at the point (-1, 1).