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Compared to the parent function f(x) = x², how has the graph f (x) = x² - 9 been translated?
A) It has been rotated -9 units.
B It has been translated 9 units down.
It has been translated 9 units up.
DIt has been translated 9 units to the left.
E It has been translated 9 units to the right.

Sagot :

GinnyAnsweridn
To determine how the graph of the function [tex]\( f(x) = x^2 \)[/tex] has been translated, let's analyze the function [tex]\( f(x) = x^2 - 9 \)[/tex].

First, recall the parent function:
[tex]\[ f(x) = x^2 \][/tex]

This function represents a standard parabola that opens upwards with its vertex at the origin [tex]\((0, 0)\)[/tex].

Next, consider the given function:
[tex]\[ f(x) = x^2 - 9 \][/tex]

When comparing this to the parent function [tex]\( f(x) = x^2 \)[/tex], it's evident that we are subtracting 9 from the output of the function.

Subtracting a constant from the function causes a vertical translation of the graph. Specifically, subtracting 9 means every point on the graph of [tex]\( f(x) = x^2 \)[/tex] is moved 9 units downward.

Thus, the transformation that has occurred is a vertical translation of 9 units down.

### Answer:
B) It has been translated 9 units down.
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