SOLUTION: Name the x-intercepts of the graph of f(x)=x^2+4x+1. Can you show me this please.

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Question 202497: Name the x-intercepts of the graph of f(x)=x^2+4x+1. Can you show me this please.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
x intercepts happen with f(x) = 0
So solve this for x
0+=+x%5E2%2B4x%2B1
Use this URL to help you --> http://www.algebra.com/algebra/homework/quadratic/quadratic.solver
Solved by pluggable solver: SOLVE quadratic equation with variable
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%2A1%2A1=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+-0.267949192431123
x%5B2%5D+=+%28-%284%29-sqrt%28+12+%29%29%2F2%5C1+=+-3.73205080756888

Quadratic expression 1x%5E2%2B4x%2B1 can be factored:
1x%5E2%2B4x%2B1+=+1%28x--0.267949192431123%29%2A%28x--3.73205080756888%29
Again, the answer is: -0.267949192431123, -3.73205080756888. 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