SOLUTION: Can you PLEASE show me how to graph a quadratic function using its properties? p(x)=-x^2+2x-5 Thank You!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you PLEASE show me how to graph a quadratic function using its properties? p(x)=-x^2+2x-5 Thank You!      Log On


   

Question 171209: Can you PLEASE show me how to graph a quadratic function using its properties?
p(x)=-x^2+2x-5 Thank You!
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B2x%2B-5+=+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=%282%29%5E2-4%2A-1%2A-5=-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+=+%28-2%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C-1+=++%28-2%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%2B2%2Ax%2B-5+%29


Because the squared term is - the parabola is upside down.