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Beginning with the graph of f(x) = x2, what transformations are needed to form g(x) = -(x - 6)2 + 3?
O The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.

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The graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units.

How to apply rigid transformations on a given function

Let be [tex]f(x) = x^{2}[/tex], we need to apply the following three rigid transformations on [tex]f(x)[/tex] to obtain [tex]g(x)[/tex]:

  1. Reflection around the x-axis: [tex]f'(x) = -x^{2}[/tex]
  2. Translation in the +x semiaxis: [tex]f''(x) = -(x-6) ^{2}[/tex]
  3. Translation in the +y semiaxis: [tex]g(x) = -(x-6) ^{2}+3[/tex]

Hence, the graph of [tex]g(x)[/tex] opens downward and is shifted to the right 6 and up 3 units. [tex]\blacksquare[/tex]

To learn more on rigid transformations, we kindly invite to check this verified question: https://brainly.com/question/1761538

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