To evaluate the function [tex]\( f(x) = -3x^2 + 2x \)[/tex] at the given input [tex]\( x = -2 \)[/tex]:
1. Start by substituting [tex]\( x = -2 \)[/tex] into the function:
[tex]\[
f(-2) = -3(-2)^2 + 2(-2)
\][/tex]
2. Evaluate the squared term:
[tex]\[
(-2)^2 = 4
\][/tex]
3. Substitute this result back into the function:
[tex]\[
f(-2) = -3(4) + 2(-2)
\][/tex]
4. Perform the multiplication:
[tex]\[
-3 \times 4 = -12
\][/tex]
[tex]\[
2 \times (-2) = -4
\][/tex]
5. Combine these results:
[tex]\[
f(-2) = -12 + (-4)
\][/tex]
6. Simplify the expression by combining the terms:
[tex]\[
-12 - 4 = -16
\][/tex]
So, the value of the function [tex]\( f(x) = -3x^2 + 2x \)[/tex] when [tex]\( x = -2 \)[/tex] is [tex]\( -16 \)[/tex].
[tex]\[
f(-2) = -16
\][/tex]
