Answered

Find expert answers and community support for all your questions on IDNLearn.com. Ask anything and get well-informed, reliable answers from our knowledgeable community members.

Verify whether the cones are the same:
(i) [tex]x^2 - 2x \quad x = 2, 0[/tex]



Format the following question or task so that it is easier to read.
Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
Do not remove or change LaTeX formatting.
Do not change or remove [tex] [/tex] tags.
If the question is nonsense, rewrite it so that it makes sense.
-----
Express 3x^2 − 27 in the form a(x + b)^2 + c and hence find the maximum value of 3x^2 − 27.
-----

Response:
Express [tex]3x^2 - 27[/tex] in the form [tex]a(x + b)^2 + c[/tex] and hence find the maximum value of [tex]3x^2 - 27[/tex].

Sagot :

GinnyAnsweridn
Sure! Let's verify the values of the function [tex]\( x^2 - 2x \)[/tex] at [tex]\( x = 2 \)[/tex] and [tex]\( x = 0 \)[/tex].

### Step-by-Step Solution

1. Define the Function:
[tex]\[ f(x) = x^2 - 2x \][/tex]

2. Calculate the Function Value at [tex]\( x = 2 \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 2^2 - 2 \cdot 2 \][/tex]
- Perform the calculations:
[tex]\[ = 4 - 4 \][/tex]
- Simplify the result:
[tex]\[ = 0 \][/tex]

3. Calculate the Function Value at [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ f(0) = 0^2 - 2 \cdot 0 \][/tex]
- Perform the calculations:
[tex]\[ = 0 - 0 \][/tex]
- Simplify the result:
[tex]\[ = 0 \][/tex]

Therefore, the values of the function [tex]\( x^2 - 2x \)[/tex] at [tex]\( x = 2 \)[/tex] and [tex]\( x = 0 \)[/tex] are both:
[tex]\[ f(2) = 0 \][/tex]
[tex]\[ f(0) = 0 \][/tex]

So, the verified values are [tex]\( (0, 0) \)[/tex].
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.