Hi Di
You might want to just review the features associated with a Parabola to get an understanding why h and k are used. You should also review the Vertex and Standard(or General) forms of the Equation of a Parabola to see they how they relate to one another.
For a parabola, the x coordinate of the vertex is h and the y coordinate is k since you are given the vertex coordinates (-1, -4) you already have h, k
You just need to calculate a. You can use the point that the parabola passes through (5, 104) to find a. As was done by Yefim S above you just plug in the information you already have and solve for a.
h = -1
k = -4
P(x) = a(x - h)2 + k
When you review the features of a Parabola you will find that the line along x = h is a line that splits the parabola into two symmetric parts, this line is also called the axes of symmetry for the parabola. The Vertex Form of a parabola makes it easy to find the coordinates for the maximum or minimum of a Parabola, distinguishing them as (h,k) while defining the curve’s horizontal and vertical shift from the origin. The Standard or General form can be easier for finding the zeroes, because often it can be easily factored and directly gives the coefficients needed for the Quadratic Formula when it cannot be factored. I hope this helps.
