To find the vertex of the quadratic equation y = 2x² + 12x + 1, we can use the vertex formula. For a quadratic in the form of y = ax² + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).
In our equation, a = 2 and b = 12. Plugging these values into the formula gives:
x = -12 / (2 * 2) = -12 / 4 = -3
Now that we have the x-coordinate of the vertex, we can substitute x = -3 back into the original equation to find the y-coordinate:
y = 2(-3)² + 12(-3) + 1
This simplifies to:
y = 2(9) – 36 + 1 = 18 – 36 + 1 = -17
Thus, the vertex of the graph is at the point (-3, -17).
In conclusion, the vertex of the quadratic function y = 2x² + 12x + 1 is (-3, -17), which represents the maximum or minimum point of the parabola, depending on the direction it opens.