
Step-by-step explanation:
The vertex form of the equation for a parabola is given by

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

or

Therefore, the equation of the parabola is
