I need to find the a formula for an parabola with the vertex (1,5) and an x-intercept at (5,0)

Answer 1

If a parabola has one x-intercept, it must have 2; furthermore it must be symmetric about the ordinate of its vertex.

What is the other x-intercept?

Draw a picture and you will see that the other intercept must be (-3,0)

Now you know the roots of the equation of the parabola which will tell you what the equation is.