A point belongs to the x axis if its y coordinate equals zero.
The points on a graph are in the form [tex] (x,f(x)) [/tex], so these points are on the x axis if and only if [tex] f(x)=0 [/tex]
In this case, we have
[tex] f(x) = 0 \iff x^2+14x+49=0 [/tex]
You can observe that your expression is actually a squared binomial: using
[tex] (a+b)^2 = a^2+2ab+b^2 [/tex]
you can notice that
[tex] (x+7)^2 = x^2+14x+49 [/tex]
So, you have
[tex] x^2+14x+49=0 \iff (x-7)^2 = 0 \iff x=7 [/tex]
Now, how we decide if this function "touches" or "passes through" the x-axis at x=7? Well, since our function is a square, it is never negative. So, this graph can't cross the x-axis, but rater touch it from above. The parabola has a U shape, and the point of minimum lies on the x axis.
So, the graph touches the x axis at x=7.
