Question

use transformations of $f(x)=x^2$ to graph the following function.\\
$g(x)=x^2 + 4$\\
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what transformation is needed to graph the function $g(x)=x^2 + 4$? choose the correct answer below.\\
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a. the graph of $f(x)=x^2$ should be shifted 4 units to the left.\\
b. the graph of $f(x)=x^2$ should be shifted 4 units to the right.\\
c. the graph of $f(x)=x^2$ should be shifted 4 units down.\\
d. the graph of $f(x)=x^2$ should be shifted 4 units up.\\
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use the graphing tool to graph the function.\\
click to enlarge graph

Explanation:

For a parent function $f(x) = x^2$, a transformation of the form $g(x) = f(x) + k$ results in a vertical shift. When $k>0$, the graph shifts upward by $k$ units. Here, $k=4$, so the graph of $f(x)=x^2$ shifts 4 units up.

Answer:

D. The graph of $f(x)=x^2$ should be shifted 4 units up.