QuestionWhat is the new equation for $g(x)=4 x^{2}-16$ after shifting it 7 right and 3 down?

Studdy Solution

STEP 1

Assumptions1. The original function is $g(x)=4x^{}-16$ . The function is shifted7 units to the right and3 units down

STEP 2

To shift a function to the right, we subtract the shift amount from the variable inside the function. So, to shift $g(x)$ 7 units to the right, we replace $x$ with $(x-7)$ .
$h(x)=4(x-7)^{2}-16$

STEP 3

To shift a function down, we subtract the shift amount from the entire function. So, to shift $h(x)$ 3 units down, we subtract3 from the function.
$h(x)=(x-7)^{2}-16-3$

STEP 4

implify the equation.
$h(x)=4(x-7)^{2}-19$ So, the new equation after shifting $g(x)$ 7 units to the right and3 units down is $h(x)=4(x-7)^{2}-19$ . The correct answer is option B.

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