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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.

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sqdancefan

Answer:

  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

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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