To find the vertex of the quadratic equation in the form of y = ax² + bx + c, we use the vertex formula. The x-coordinate of the vertex can be calculated using the formula:
x = -b / (2a)
For the given equation, y = 3x² + 12x + 5, we identify:
- a = 3
- b = 12
- c = 5
Plugging these values into the vertex formula:
x = -12 / (2 * 3) = -12 / 6 = -2
Now that we have the x-coordinate of the vertex, we need to find the y-coordinate. To do this, substitute x = -2 back into the original equation:
y = 3(-2)² + 12(-2) + 5
y = 3(4) – 24 + 5
y = 12 – 24 + 5 = -7
Thus, the vertex of the graph of the equation y = 3x² + 12x + 5 is:
(-2, -7)