# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #f(x)=1/3(x+6)^2+5#?

Expand the equation and simplify it and then complete the square.

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To find the axis of symmetry of the function (f(x) = \frac{1}{3}(x + 6)^2 + 5), use the formula (x = -\frac{b}{2a}), where (a = \frac{1}{3}) and (b = 6). The axis of symmetry is (x = -\frac{6}{2(\frac{1}{3})}), which simplifies to (x = -6).

The graph of the function is a parabola that opens upwards because the coefficient of (x^2) is positive. The vertex of the parabola is at the point ((-6, 5)), which corresponds to the axis of symmetry.

To find the maximum or minimum value of the function, observe that the coefficient of (x^2) is positive, indicating a minimum value. The minimum value occurs at the vertex, which is (f(-6) = 5). Therefore, the minimum value of the function is (5).

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