SOLUTION: y=-(x+3)^2-4

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Question 920724: y=-(x+3)^2-4

Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
y= -(x+3)^2 -4
y =-(x+3)*(x+3) -4
y = -(x(x+3)+3(x-3) -4
y = -(x^2+3x+3x+3*3)-4
y= -(x^2+6x+9)-4
y= -X^2-6x-9-4
y =-x^2-6x-13
solve the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-6x%2B-13+=+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=%28-6%29%5E2-4%2A-1%2A-13=-16.

The discriminant -16 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 -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28--6%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C-1+=++%28--6%2B-+i%2A4%29%2F2%5C-1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-6%2Ax%2B-13+%29