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The parabola y=x^(2) is shifted down by 6 units and to the right by 5 units. What is the equation of the new parabola? y=

The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=

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Full solution

Q. The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=
  1. Shift down by 66 units: To shift the parabola y=x2y = x^2 down by 66 units, we need to subtract 66 from the yy-value of the original parabola. This gives us a new equation y=x2−6y = x^2 - 6.
  2. Shift right by extbf{ extit{55}} units: Next, to shift the parabola to the right by extbf{ extit{55}} units, we need to replace extit{x} with extit{(x - 55)} in the equation. This gives us the new equation extit{y = (x - 55)^22 - 66}.

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