SOLUTION: Stuck again.... ugh:-( Can someone please help me?? f(x)= -x^2+4x+1

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Question 64052: Stuck again.... ugh:-( Can someone please help me??
f(x)= -x^2+4x+1
Answer by sarahschober(35) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B4x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A-1%2A1=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+20+%29%29%2F2%5C-1+=+-0.23606797749979
x%5B2%5D+=+%28-%284%29-sqrt%28+20+%29%29%2F2%5C-1+=+4.23606797749979

Quadratic expression -1x%5E2%2B4x%2B1 can be factored:
-1x%5E2%2B4x%2B1+=+%28x--0.23606797749979%29%2A%28x-4.23606797749979%29
Again, the answer is: -0.23606797749979, 4.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B4%2Ax%2B1+%29