Final answer:
The function described has a y-intercept and two x-intercepts with a minimum point at its vertex, indicating it is a quadratic function with a positive leading coefficient. An example of such a function is f(x) = x² + 5x + 6.
Step-by-step explanation:
The function described in the student's question has a y-intercept and two x-intercepts, and it has a minimum point at its vertex.
With the given characteristics, we are looking for a quadratic function, typically represented as f(x) = ax² + bx + c. Since it has a minimum point, the coefficient a must be positive.
The y-intercept is given by the value c, and the x-intercepts (or zeros of the function) occur where the graph of the function crosses the x-axis.
An example of such a function could be f(x) = x² + 5x + 6. It has a y-intercept at (0, 6) and x-intercepts at the points where f(x) = 0, which can be found by factoring or using the quadratic formula.
In this case, the graph of f(x) = x² + 5x + 6 would intersect at x values which would make the expression equal to zero.
Since the function is a parabola that opens upwards (due to a positive a), it also means that the vertex of the graph is at its minimum point.