Answer :
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].
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].
