I need help in identifying a graph. I tried textbook and plugging no. with no luck

Question

All numbers on right side of (y) line. Bottom of parabola is on x=4 and y=-4, going up f(x) dot is on x=3, y=-3 (left line going up); right line going up is x=5, y= -3; going up again dots on x lt side at x=2, rt side x=6; up again: lt side x=1, y=5; rt side x=7, y=5. Thanks for help.

Answer 1

man! what a lot of words! Why not just list the points on the graph?

(4,-4),(3,-3),(5,-3)
Right there we see the vertex is at (4,-4), so

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

Now we have points (1,5),(7,5)
5 = a(-3)^2 - 4 = 9a-4
a = 1

so, y = (x-4)^2 - 4