SOLUTION: graph: y = x squared - 4x - 3

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Question 167602: graph: y = x squared - 4x - 3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
graph: y = x squared - 4x - 3
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OK
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-3+=+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=%28-4%29%5E2-4%2A1%2A-3=28.

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

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+4.64575131106459
x%5B2%5D+=+%28-%28-4%29-sqrt%28+28+%29%29%2F2%5C1+=+-0.645751311064591

Quadratic expression 1x%5E2%2B-4x%2B-3 can be factored:
1x%5E2%2B-4x%2B-3+=+%28x-4.64575131106459%29%2A%28x--0.645751311064591%29
Again, the answer is: 4.64575131106459, -0.645751311064591. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-3+%29

To be more clear, the solutions are:
2+%2B+sqrt%287%29 and
2+-+sqrt%287%29