The graph of the quadratic parent function is reflected across the x-axis, then shifted 5 units down and 4 units right. write the equation of the new function in vertex form.

This is about reflection of graphs.

y = -(x - 4)² + 5

We are told the graph is that of the quadratic parent function. Now, in transformations of quadratic functions, the parent function of the quadratic group is usually expressed as;

y = x²

       -y = x²

-y = x² - 5

-y = (x - 4)² - 5

Dividing through by -1 to get;

y = -(x - 4)² + 5

Read more at; link

  y = -(x -4)² -5

Step-by-step explanation:

-f(x) is a reflection of f(x) across the x-axis.

f(x) -5 is a translation down by 5 units.

f(x -4) is a translation right by 4 units.

Applying these transformations to y = x² gives, successively, ...

  y = -x²

  y = -x² -5

  y = -(x -4)² -5 . . . . . . the new equation in vertex form