To find [tex]\( f(-2) \)[/tex] for the function [tex]\( f(x) = x^2 + 2x - 10 \)[/tex], follow these steps:
1. Substitute [tex]\(-2\)[/tex] into the function:
[tex]\[
f(-2) = (-2)^2 + 2(-2) - 10
\][/tex]
2. Calculate the square of [tex]\(-2\)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
3. Multiply [tex]\(2\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[
2 \cdot (-2) = -4
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
f(-2) = 4 + (-4) - 10
\][/tex]
5. Perform the addition and subtraction:
[tex]\[
f(-2) = 4 - 4 - 10 = -10
\][/tex]
Therefore, [tex]\( f(-2) = -10 \)[/tex].
Thus, the correct answer is [tex]\(-10\)[/tex].
