The vertex of a quadratic function in the form f(x) = ax² + bx + c can be found using the formula for the x-coordinate of the vertex, which is given by x = -b / (2a). In this case:
- a = 3
- b = 6
- c = 3
Plugging in the values:
x = -6 / (2 * 3) = -6 / 6 = -1
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x back into the function:
f(-1) = 3(-1)² + 6(-1) + 3
f(-1) = 3(1) – 6 + 3 = 3 – 6 + 3 = 0
Thus, the coordinates of the vertex are (-1, 0).