To solve for [tex]\( f(8) \)[/tex] using the quadratic function [tex]\( f(x) = 25x^2 - 28x + 585 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 8 \)[/tex] into the function:
[tex]\[
f(8) = 25(8)^2 - 28(8) + 585
\][/tex]
2. Calculate [tex]\( (8)^2 :
\[
(8)^2 = 64
\]
3. Multiply 64 by 25:
\[
25 \times 64 = 1600
\]
4. Multiply 28 by 8:
\[
28 \times 8 = 224
\]
5. Substitute these values back into the equation:
\[
f(8) = 1600 - 224 + 585
\]
6. Perform the subtraction and addition:
\[
1600 - 224 = 1376
\]
\[
1376 + 585 = 1961
\]
So, the value of \( f(8) \)[/tex] is [tex]\( 1961 \)[/tex].
Therefore, the correct value from the given options is:
[tex]\( f(8) = 1961 \)[/tex].
