What kind of transformation converts the graph of f(x) = –3x^2 – 4 into the graph of g(x) = –3x^2 + 6? Choices: [[translation 10 units up][translation 10 units down][translation 10 units left][translation 10 units right]]

Identify transformation: Identify the transformation needed to go from f(x) = –3x^2 – 4 to g(x) = –3x^2 + 6. Notice change in constant: Notice the only change is in the constant term, from -4 in f(x) to +6 in g(x). This indicates a vertical shift. Calculate difference for shift: Calculate the difference between the constant terms to find the magnitude of the shift. Difference = 6 - (-4) = 10. Determine direction of shift: Determine the direction of the shift. Since the constant term increased, the shift is upwards.

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

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Math Problems

Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

Choices:

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

\newline

\text{[D]translation 10 units right}

Identify transformation: Identify the transformation needed to go from $f(x) = -3x^2 - 4$ to $g(x) = -3x^2 + 6$ .
Notice change in constant: Notice the only change is in the constant term, from $-4$ in $f(x)$ to $+6$ in $g(x)$ . This indicates a vertical shift.
Calculate difference for shift: Calculate the difference between the constant terms to find the magnitude of the shift. Difference = $6 - (-4) = 10$ .
Determine direction of shift: Determine the direction of the shift. Since the constant term increased, the shift is upwards.