The graph above is the graph of y=x2 translated and reflected in the xy-plane. Find an equation for this graph.

Thanks for the answer! I have a question though. Shifting it to the left makes it -7, so how does it turn positive?

This is always confusing....

Note that  we have

(x + 7)^2 + 4

The form that we are really going for is

( x - h)^2 + k        where ( h, k) is the vertex

So....

(x - (-7) )^2 + 4     produces the vertex (h, k)  =  (-7, 4)

But this is just the same as

(x + 7)^2 + 4

Remember that a " + "  moves the x coordinate of the vertex to the left  and a " - "  moves the x coordinate of the vertex to the right

To get a feel for this....look at the graph here :  https://www.desmos.com/calculator/4ryl8slhym

y = ( x + 2)^2  shifts the vertex of y = x^2 to the left 2 units

y = ( x - 2)^2  shifts the vertex of y = x^2 to the right by 2 units

You're responses are so thorough! Thank you so much for taking the time to explain it in detail, I really appreciate it. It's a whole lot clearer to me now

OK....glad to help....