High School

We appreciate your visit to Select the correct answer Which of these is the standard form of the following function Given function tex f x 9 x 5 2 4. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Select the correct answer.

Which of these is the standard form of the following function?

Given function: [tex]f(x) = -9(x+5)^2 + 4[/tex]

A. [tex]f(x) = -9x^2 - 90x - 221[/tex]
B. [tex]f(x) = -9x^2 - 180x - 221[/tex]
C. [tex]f(x) = 9x^2 - 180x + 221[/tex]
D. [tex]f(x) = 9x^2 - 90x - 221[/tex]

Answer :

To find the standard form of the function [tex]\( f(x) = -9(x+5)^2 + 4 \)[/tex], we'll need to expand the expression. Here's how you can do it step by step:

1. Start with the squared term:
The function inside the parentheses is [tex]\( (x + 5)^2 \)[/tex]. Expanding this, we have:
[tex]\[
(x + 5)^2 = x^2 + 10x + 25
\][/tex]

2. Multiply by -9:
Now, multiply each term in the expanded form by -9:
[tex]\[
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225
\][/tex]

3. Add the constant term (+4):
Add the 4 from the original function to the expanded expression:
[tex]\[
-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221
\][/tex]

Thus, the standard form of the function is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]

The correct answer is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]

Thanks for taking the time to read Select the correct answer Which of these is the standard form of the following function Given function tex f x 9 x 5 2 4. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada