To find the vertex of the quadratic function represented by the equation y = 2x² + 12x + 3, we can use the vertex formula or complete the square.
The vertex of a parabola given in the form y = ax² + bx + c can be found using the formula for x-coordinate of the vertex: x = -b / (2a). Here, a = 2 and b = 12.
Plugging in the values, we get:
x = -12 / (2 * 2) = -12 / 4 = -3
Next, we need to find the y-coordinate of the vertex by substituting x back into the original equation:
y = 2(-3)² + 12(-3) + 3
y = 2(9) – 36 + 3
y = 18 – 36 + 3 = -15
Therefore, the vertex of the graph is at the point (-3, -15).