Step 1. The vertex of the parabola is:
(-4,5)
And one of the x-intercepts i:
(2,0)
They are shown in the following diagram (not to scale):
Step 2. We are asked to find the other x-intercept. To find it, we use the symmetry of the parabola:
There must be the same distance between the vertex and each x-intercept.
To represent that distance we draw a triangle between the known vertex and x-intercept:
That triangle has a side of 5 and a side of 6 units.
Step 3. We draw the same triangle but to the left side of the vertex to find the other x-intercept:
We end up at (-10,0) this is the other x-intercept.
Answer:
(-10, 0)