A parabola opening upward shifted 7 units rights and 4 units down

y + 4 = a (x - 7) ^2

Step-by-step explanation:

The standard vertex form of a parabola with vertex at (h, k) is

y - k = a (x - h) ^2

and if we start with the simplest case, y = a (x) ^2 and translate its graph 7 units to the right and 4 units down, we get y - {-4] = a (x - 7) ^2, or

y + 4 = a (x - 7) ^2