Which function's graph is symmetric about the point (0,−4)

Question

Which function's graph is symmetric about the point (0,−4)

Answer 1

Jordan:

Symmetric about point (0,-4) means the distance between the graph f(x) and point (0,-4) will always equal the distance between point (0,-4) and the symmetric line.

For example, if (0,-2) lies on f(x), then the point (0,-6) lies on the symmetric line because the distance between (0,-2) and (0,-4) equals the distance between (0,-4) and (0,-6), in this case 2.

What about another point, say (1,0) lies of f(x). Distance to (0,-4) is √17. So the corresponding point on the symmetric line must be at a distance of √17 form (0,-4) on the imaginary line connecting the symmetric point, point (0,-4), and the point on f(x).

Please let me know if you need help!

Answer 2

You want a parabola with a vertex at the point (0,-4) so that is symmetrical on each side of that point. Using the point (0,-4), write the equation for a parabola in vertex form and then simplify:

vertex = (h,k) = (0,-4)

y = (x - h)² + k = (x - 0)² - 4 = x² - 4