Answer
no x-intercepts, 1 y-intercept
Work Step by Step
We are told the parabola opens up and has its vertex in quadrant I.
With the vertex in quadrant I, we know either the $x$ value of the vertex is greater than zero or the $y$ value of the vertex is greater than zero (or both are true).
Since at least one coordinate of the vertex is positive, and the parabola opens up, the graph of the parabola doesn't cross the x-axis. Since the graph doesn't cross the x-axis, there are no x-intercepts.
Since at least one coordinate of the vertex is positive, and the parabola opens up, the graph of the parabola does cross the y-axis. Since the graph does cross the y-axis, there is one x-intercept.
