Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

A. [tex]h(x) = 4(x - 17)^2 - 9[/tex]
B. [tex]h(x) = 4(x - 7)^2 + 16[/tex]
C. [tex]h(x) = 4(x - 9)^2 - 17[/tex]
D. [tex]h(x) = 4(x + 9)^2 - 17[/tex]


Sagot :

Sure, let's solve this step by step.

We start with the given function:
[tex]\[ g(x) = 4x^2 - 16 \][/tex]

Our objective is to perform two transformations on [tex]\( g(x) \)[/tex]:
1. Shift it 9 units to the right.
2. Shift it 1 unit down.

Step 1: Shifting 9 units to the right

To shift the graph of a function [tex]\( g(x) \)[/tex] horizontally to the right by [tex]\( c \)[/tex] units, we replace [tex]\( x \)[/tex] with [tex]\( x - c \)[/tex]. Here, [tex]\( c = 9 \)[/tex], so we replace [tex]\( x \)[/tex] with [tex]\( x - 9 \)[/tex]:

[tex]\[ g(x - 9) = 4(x - 9)^2 - 16 \][/tex]

Step 2: Shifting 1 unit down

To shift the graph of a function vertically downward by [tex]\( c \)[/tex] units, we subtract [tex]\( c \)[/tex] from the entire function. Here, [tex]\( c = 1 \)[/tex], so we subtract 1 from [tex]\( g(x - 9) \)[/tex]:

[tex]\[ h(x) = 4(x - 9)^2 - 16 - 1 \][/tex]

Simplifying the expression:

[tex]\[ h(x) = 4(x - 9)^2 - 17 \][/tex]

Thus, the new equation after the shifts is:

[tex]\[ h(x) = 4(x - 9)^2 - 17 \][/tex]

Comparing this with the given options, the correct answer is:

C. [tex]\( h(x) = 4(x - 9)^2 - 17 \)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.