Question Show Examples Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer is an $(x, y)$ point. \[ y=3 x^{2}+12 \] Answer Attempt 2 out of 3 Submit Answer

Step 1 ：The vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is at the point \((-b/2a, f(-b/2a))\), where \(f(x)\) is the function defined by the equation of the parabola.

Step 2 ：In this case, the equation of the parabola is \(y = 3x^2 + 12\), so \(a = 3\) and \(b = 0\). Therefore, the x-coordinate of the vertex is \(-b/2a = -0/(2*3) = 0\).

Step 3 ：Substituting \(x = 0\) into the equation of the parabola gives the y-coordinate of the vertex as \(y = 3*0^2 + 12 = 12\).

Step 4 ：Therefore, the vertex of the parabola is at the point \((0, 12)\).

Step 5 ：\(\boxed{(0, 12)}\) is the vertex of the parabola.