Answer :
To find the value of the function [tex]\( f(x) = -x^2 \cdot (3x + 2)^2 \)[/tex] at [tex]\( x = -2 \)[/tex], follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the function:
[tex]\[ f(-2) = -(-2)^2 \cdot (3(-2) + 2)^2 \][/tex]
2. Calculate [tex]\((-2)^2\)[/tex]:
[tex]\((-2)^2 = 4\)[/tex].
3. Calculate [tex]\(3(-2) + 2\)[/tex]:
First, multiply [tex]\(3 \times (-2)\)[/tex] which gives [tex]\(-6\)[/tex].
Then, [tex]\(-6 + 2 = -4\)[/tex].
4. Square [tex]\(-4\)[/tex]:
[tex]\((-4)^2 = 16\)[/tex].
5. Combine the results:
Multiply the results from steps 2 and 4, with the negative sign:
[tex]\[ f(-2) = -(4) \cdot (16) \][/tex]
6. Calculate the final value:
[tex]\(-4 \times 16 = -64\)[/tex].
Therefore, the value of [tex]\( f(-2) \)[/tex] is [tex]\(-64\)[/tex].
The correct answer is: E. -64
1. Substitute [tex]\( x = -2 \)[/tex] into the function:
[tex]\[ f(-2) = -(-2)^2 \cdot (3(-2) + 2)^2 \][/tex]
2. Calculate [tex]\((-2)^2\)[/tex]:
[tex]\((-2)^2 = 4\)[/tex].
3. Calculate [tex]\(3(-2) + 2\)[/tex]:
First, multiply [tex]\(3 \times (-2)\)[/tex] which gives [tex]\(-6\)[/tex].
Then, [tex]\(-6 + 2 = -4\)[/tex].
4. Square [tex]\(-4\)[/tex]:
[tex]\((-4)^2 = 16\)[/tex].
5. Combine the results:
Multiply the results from steps 2 and 4, with the negative sign:
[tex]\[ f(-2) = -(4) \cdot (16) \][/tex]
6. Calculate the final value:
[tex]\(-4 \times 16 = -64\)[/tex].
Therefore, the value of [tex]\( f(-2) \)[/tex] is [tex]\(-64\)[/tex].
The correct answer is: E. -64
