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

Now, we are told that this quadratic parent function is reflected across the x-axis. This means the value of the y-coordinate will become negative and we have;

       -y = x²

It is now shifted 5 units down. This means we will now have;

-y = x² - 5

It is now shifted 4 units down. This means we now have;

-y = (x - 4)² - 5

Dividing through by -1 to get;

y = -(x - 4)² + 5

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  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

Subtract from the dividend an easy multiple of the divisor

Record the partial quotient in a column to the right of the problem.

Repeat until the dividend has been reduced to zero or the remainder is less than the divisor.

Add the partial quotients to find the quotient.

Step-by-step explanation:

Hope this helps :)