Let's break down each part of your question step by step.
-
Equivalent expression for
To simplify
: So the expression equivalent to is 10 square root of 6. -
Value of
whereSubstitute
into the function: -
Value of
whereSubstitute
into the function: -
Expressions equivalent to
Let's factor
: So one correct answer is 12(x − 2)².Now let's examine the other options for correctness:
- −12(x² + 4x + 4): This is equivalent to
, which is not equivalent. - 12(x − 4)(x − 1): This is not equivalent, as this expands to
. - −12(x + 2)²: This is not equivalent, as it represents a reflection and different dimensions.
- 12(x² − 4x + 4): This expression is the same as what we factored, thus is also equivalent.
- −12(x² + 4x + 4): This is equivalent to
So, the two correct responses are:
- 12(x − 2)²
- 12(x² − 4x + 4)
In summary:
- Equivalent to
: 10 square root of 6 - Value of
: 282 - Value of
: -7 - Equivalent expressions: 12(x − 2)² and 12(x² − 4x + 4).