SOLUTION: given the function f(x)=-x^2+2x-3 find f(2)-2*f(0)

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Question 216931: given the function f(x)=-x^2+2x-3
find f(2)-2*f(0)
Found 2 solutions by Earlsdon, MathTherapy:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
f%28x%29+=+x%5E2%2B2x-3 find:
f%282%29-2f%280%29
f%282%29+=+%282%29%5E2%2B2%282%29-3
f%282%29+=+4%2B4-3
f%282%29+=+5
f%280%29+=+0%5E2%2B2%280%29-3
f%280%29+=+-3
f%282%29-2f%280%29+=+5-2%28-3%29
f%282%29-2f%280%29+=+5%2B6
highlight%28f%282%29-2f%280%29+=+11%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
given the function f(x)=-x^2+2x-3
find f(2)-2*f(0)

Since f%28x%29+=+-+x%5E2+%2B+2x+-+3, then f%282%29+=+-+%282%29%5E2+%2B+2%282%29+-+3+=+-+4+%2B+4+-+3+=+-+3

Since f%28x%29+=+-+x%5E2+%2B+2x+-+3, then 2%2Af%280%29+=+2+%2A+%280+%2B+0+-+3%29+=+2+%2A+%28-+3%29+=+-+6

Therefore, f(2)-2*f(0) = - 3 - (- 6) = - 3 + 6 = highlight_green%283%29