To find [tex]\( h(4) \)[/tex] for the function [tex]\( h(n) = -2n^2 + 4 \)[/tex]:
1. Substitute [tex]\( n = 4 \)[/tex] into the given function:
[tex]\[ h(4) = -2(4)^2 + 4 \][/tex]
2. Simplify the expression inside the parentheses first:
[tex]\[ (4)^2 = 16 \][/tex]
3. Substitute this back into the equation:
[tex]\[ h(4) = -2 \cdot 16 + 4 \][/tex]
4. Multiply [tex]\(-2\)[/tex] by [tex]\(16\)[/tex]:
[tex]\[ -2 \cdot 16 = -32 \][/tex]
5. Add [tex]\(4\)[/tex] to [tex]\(-32\)[/tex]:
[tex]\[ h(4) = -32 + 4 \][/tex]
6. Simplifying the above expression gives:
[tex]\[ h(4) = -28 \][/tex]
So, [tex]\( h(4) = -28 \)[/tex].
