Final answer:
The function h(x) = ½x² - 7x + 7 is a quadratic function that opens upwards, indicating it has a minimum value. The minimum can be found by calculating the vertex of the parabola using the formula -b/(2a).
Step-by-step explanation:
For the function h(x) = ½x² - 7x + 7, we are asked to determine if the function has a maximum or minimum value. To do this, we identify that h(x) is a quadratic function in the form of ax² + bx + c, where a, b, and c are constants. In this function, a is positive (½), which indicates the parabola opens upwards, and therefore, the graph of this function will have a minimum point.
To find the minimum value of h(x), we calculate the vertex of the parabola. The x-coordinate of the vertex can be found using the formula -b/(2a). Substituting the values from h(x), we get -(-7) / (2 · ½), which simplifies to 7. We then plug this x-value into the function to find the y-coordinate of the vertex, h(7), which will give us the minimum value of the function. After performing these calculations, we would have the coordinates of the vertex, which indicates the minimum point of the quadratic function h(x), on the graph of the parabola.