Final answer:
The minimum value of the equation y = (1/3)x² + 2x + 5 is found using the vertex of the parabola, which occurs at x = -3. By substituting x = -3 back into the equation, we find that the minimum value is y = 2.
Step-by-step explanation:
The minimum value of the equation y = (1/3)x² + 2x + 5 is found using the vertex form of a parabola. Since the equation is in the form of y = ax² + bx + c, where a > 0, the parabola opens upwards, and the vertex represents the minimum point.
To find the vertex, we can use the vertex formula x = -b/(2a). Substituting the values from our equation, b = 2 and a = 1/3, into the formula gives us x = -2/(2*(1/3)) = -3. To find the minimum value (the y-value of the vertex), we substitute x = -3 back into the original equation:
y = (1/3)(-3)² + 2*(-3) + 5
y = (1/3)*9 - 6 + 5
y = 3 - 6 + 5
y = 2
So, the minimum value of the equation is 2.