Answered

IDNLearn.com provides a collaborative environment for finding accurate answers. Ask anything and receive prompt, well-informed answers from our community of experienced experts.

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 appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.