The y-coordinate of a point of intersection with the x-axis is 0, then for the first function, g(x) = x² + x - 2, we can find its x-intercepts by replacing 0 for g(x), then we get:
0 = x² + x - 2
By applying the quadratic we can identify two solutions for the above expression, that i,s x = -2 and x = 1, then the function g(x) = x² + x - 2 has two x-intercepts (-2, 0) and (1, 0).
The second function f(x) has only one x-intercept since its vertex is located at (2, 0), if the vertex of a parabola intersects the x-axis this is the only point of intersection with the x-axis.
As you can see in the graph, the third function h(x) has no x-intercept its vertex is located above the x-axis and it opens upward