SOLUTION: Find the axis of symmetry y=-x^2-x-7

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Question 40444: Find the axis of symmetry
y=-x^2-x-7
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
y=-x%5E2-x-7
Axis of symmetry: x+=+-b%2F%282a%29
x+=+1%2F%282%28-1%29%29
x+=+-1%2F2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-1x%2B-7+=+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=%28-1%29%5E2-4%2A-1%2A-7=-27.

The discriminant -27 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -27 is + or - sqrt%28+27%29+=+5.19615242270663.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-1%2Ax%2B-7+%29