To find the vertex of the quadratic function given by the equation y = 3x² + 12x + 3, we can use the vertex formula. The vertex form of a quadratic function is given by:
y = a(x – h)² + k
Where (h, k) are the coordinates of the vertex. Alternatively, we can find the x-coordinate of the vertex using the formula:
x = -b / (2a)
In our function, a = 3 and b = 12. Plugging these values into the formula gives us:
x = -12 / (2 * 3) = -12 / 6 = -2
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x = -2 back into the original equation:
y = 3(-2)² + 12(-2) + 3
Calculating this, we get:
y = 3(4) + 12(-2) + 3 = 12 – 24 + 3 = -9
Therefore, the coordinates of the vertex of the graph of the function y = 3x² + 12x + 3 are (-2, -9).