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The parabola y=x^(2) is shifted up by 2 units and to the right by 3 units. What is the equation of the new parabola? y=

The parabola y=x2y=x^{2} is shifted up by 22 units and to the right by 33 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 up by 22 units and to the right by 33 units.\newlineWhat is the equation of the new parabola?\newliney=y=
  1. Add 22 units: To shift the parabola y=x2y=x^2 up by 22 units, we add 22 to the original equation.\newliney=x2+2y = x^2 + 2
  2. Replace xx with (x−3)(x - 3): To shift the parabola to the right by 33 units, we replace xx with (x−3)(x - 3) in the original equation.\newliney=(x−3)2+2y = (x - 3)^2 + 2
  3. Final equation: Now we have the equation of the new parabola after applying both transformations.\newliney=(x−3)2+2y = (x - 3)^2 + 2 is the final equation.

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