Question

If g(x) =4x^2-16 were shifted 9 units to the right and 1 down, what would be the new equation

Answer 1

$h(x)=4(x-9)^2-16-1\\\\h(x)=4(x^2-18x+81)-17\\\\h(x)=4x^2-72x+324-17\\\\h(x)=4x^2-72x+307$

Answer 2

Answer: $g(x)=4x^{2} -72x+307$

Step-by-step explanation: to shift a function to the right, we need to subtract as many units as we want to shift from the x (internal function), so if we want to shift the function 9 units to the right, we subtract 9 from the x. To shift a funtion down we need to subtract as many units as we want from the whole function (external function), so in order to shift the function 1 unit down, we subtract 1 from the function:

$g(x)=4x^{2}-16$

shifting to the right:

$g(x)=4(x-9)^{2}-16$

shifting down:

$g(x)=4(x-9)^{2}-16-1$

solving the square and the products:

$g(x)=4x^{2} -72x+324-16-1$

$g(x)=4x^{2} -72x+307$