Question

Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

Answer 1

y = 0 for the x-intercept(s)

Answer 2

x = 0 for the y-intercept(s)

Answer 3

where is the parabola?

Answer 4

Looks like the logical approach is to find the equation of the parabola first. You are told, "Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6)."
The standard equation of a parabola relevant to this case is y-k=a(x-h)^2, where (h,k) represents the vertex and (x,y) is a point on the parabola.

Insert the given info about vertex and point, solving the resulting equation for the coefficient, a.

Write out the equation for this particular parabola.

Now let y=0 and solve for x. That is / are your horizontal intercept(s).