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What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}

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Q. What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}
  1. Identify transformation: Identify the transformation needed to go from f(x)=−3x2−4f(x) = -3x^2 - 4 to g(x)=−3x2+6g(x) = -3x^2 + 6.
  2. Notice change in constant: Notice the only change is in the constant term, from −4-4 in f(x)f(x) to +6+6 in g(x)g(x). This indicates a vertical shift.
  3. Calculate difference for shift: Calculate the difference between the constant terms to find the magnitude of the shift. Difference = 6−(−4)=106 - (-4) = 10.
  4. Determine direction of shift: Determine the direction of the shift. Since the constant term increased, the shift is upwards.

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