To find [tex]\( f(12) \)[/tex] for the function [tex]\( f(x) = 2x^2 + 5x - 17 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 12 \)[/tex] into the function [tex]\( f(x) \)[/tex].
So, [tex]\( f(12) = 2(12)^2 + 5(12) - 17 \)[/tex].
2. Compute the exponentiation.
Calculate [tex]\( 12^2 \)[/tex]:
[tex]\[ 12^2 = 144 \][/tex]
3. Multiply by 2.
Calculate [tex]\( 2 \times 144 \)[/tex]:
[tex]\[ 2 \times 144 = 288 \][/tex]
4. Multiply 5 by 12.
Calculate [tex]\( 5 \times 12 \)[/tex]:
[tex]\[ 5 \times 12 = 60 \][/tex]
5. Add the results from steps 3 and 4.
So, [tex]\( 288 + 60 = 348 \)[/tex]
6. Subtract 17 from the result of step 5.
Calculate [tex]\( 348 - 17 \)[/tex]:
[tex]\[ 348 - 17 = 331 \][/tex]
Therefore, [tex]\( f(12) = 331 \)[/tex].
