SOLUTION: Solve and Graph: y = -x^2 - 3x -2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve and Graph: y = -x^2 - 3x -2      Log On


   

Question 18828: Solve and Graph:
y = -x^2 - 3x -2
Answer by Alwayscheerful(414) 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%2B-3x%2B-2+=+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=%28-3%29%5E2-4%2A-1%2A-2=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+1+%29%29%2F2%5C-1+=+-2
x%5B2%5D+=+%28-%28-3%29-sqrt%28+1+%29%29%2F2%5C-1+=+-1

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

Hope this helps!