SOLUTION: Graph each equation. Label the vertex, focus and directrix x^2-6x+10y=1

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Question 39958: Graph each equation. Label the vertex, focus and directrix
x^2-6x+10y=1
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-6x%2B10y=1
x%5E2-6x-1=-10y
%28-1%2F10%29x%5E2%2B%283%2F5%29x%2B%281%2F10%29+=+y
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -.1x%5E2%2B0.6x%2B.1+=+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=%280.6%29%5E2-4%2A-.1%2A.1=0.4.

Discriminant d=0.4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.6%2B-sqrt%28+0.4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.6%29%2Bsqrt%28+0.4+%29%29%2F2%5C-.1+=+-0.16227766016838
x%5B2%5D+=+%28-%280.6%29-sqrt%28+0.4+%29%29%2F2%5C-.1+=+6.16227766016838

Quadratic expression -.1x%5E2%2B0.6x%2B.1 can be factored:
-.1x%5E2%2B0.6x%2B.1+=+-.1%28x--0.16227766016838%29%2A%28x-6.16227766016838%29
Again, the answer is: -0.16227766016838, 6.16227766016838. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-.1%2Ax%5E2%2B0.6%2Ax%2B.1+%29

You should be able to pick the information from what is above.