To evaluate the function [tex]\( f(x) = -3x^2 - 7x + 4 \)[/tex] at [tex]\( x = -2 \)[/tex], follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( f(x) \)[/tex].
[tex]\[ f(-2) = -3(-2)^2 - 7(-2) + 4 \][/tex]
2. Compute the square of [tex]\(-2\)[/tex].
[tex]\[ (-2)^2 = 4 \][/tex]
3. Multiply [tex]\(-3\)[/tex] by the result of the squared term.
[tex]\[ -3 \cdot 4 = -12 \][/tex]
4. Multiply [tex]\(-7\)[/tex] by [tex]\(-2\)[/tex].
[tex]\[ -7 \cdot (-2) = 14 \][/tex]
5. Add these results together with the constant term [tex]\(+ 4\)[/tex].
[tex]\[ -12 + 14 + 4 \][/tex]
6. Perform the addition step-by-step:
- First, combine [tex]\(-12\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[ -12 + 14 = 2 \][/tex]
- Next, add [tex]\(2\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[ 2 + 4 = 6 \][/tex]
Therefore, the value of the function [tex]\( f(-2) \)[/tex] is [tex]\( 6 \)[/tex]. The correct answer is:
[tex]\[ 6 \][/tex]
