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3 months ago

If g(x)=4x^2-16 were shifted 5 units to the right and 2 down, what would the new equation be?

Mathematics

2 answers:

Svet_ta [12.7K]3 months ago

6 0

Answer:

A. $h(x)=4(x-5)^2-18$

Detailed explanation:

Given the function $g(x)=4x^2-16$ , we need to determine the formula when g(x) moves 5 units to the right and 2 units downward.

Recall the rules for transformations.

$f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}$

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}$

Shifting the function right by 5 units changes it to:

$g(x)=4(x-5)^2-16$

Next, shifting it down by 2 units gives:

$g(x)=4(x-5)^2-16-2$

$g(x)=4(x-5)^2-18$

Thus, option A is the correct answer.

lawyer [12.5K]3 months ago

4 0

Try this method:
When a graph shifts right, replace 'x' with 'x' minus the number.
When it shifts down, subtract the number from 'y'.
So the final equation becomes: y = 4(x - 5)² - 18.
The answer is A.

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3 months ago