To find the vertex of the quadratic function given by the equation y = 3x² + 12x + 5, we can use the vertex formula. The vertex of a parabola in the form y = ax² + bx + c is found using the formula:
x = -b / (2a)
In this equation, a = 3 and b = 12. Plugging these values into the vertex formula gives us:
x = -12 / (2 * 3) = -12 / 6 = -2
Now that we have the x-coordinate of the vertex, we can find the corresponding y-coordinate by substituting x = -2 back into the original equation:
y = 3(-2)² + 12(-2) + 5
y = 3(4) – 24 + 5 = 12 – 24 + 5 = -7
Therefore, the vertex of the graph is located at (-2, -7).
In conclusion, the vertex for the graph of the given quadratic function is (-2, -7).