Question

Tell whether the function f(x)=1/2x^2-8x+13 has a minimum value or a maximum value. Then find the minimum value or maximum value.

Answer 1

The minimum value of f(x) is -19.

Explanation:

Please use parentheses around fractional coefficients to eliminate ambiguity: f(x)=(1/2)x^2-8x+13.

Because the coefficient of the x^2 term, 1/2, is positive, the graph of this quadratic opens up. Thus, the vertex represents the minimum of the function.

The equation of the axis of symmetry of this graph is x = -b / (2a). In this case, x = -(-8) / (2*[1/2]), or x = 8. Evaluating f(x) at x=8 produces the y coordinate of the vertex: f(8) = (1/2)(8^2) - 8(8) + 13 = 32 - 64 + 13 = -19.

Thus, the vertex is (8, -19). The minimum value of f(x) is -19.