SOLUTION: Graph the quadratic equation. Label the ordered pairs for the vertex and the y-intercept. y = x^2 + x -2

Algebra ->  Radicals -> SOLUTION: Graph the quadratic equation. Label the ordered pairs for the vertex and the y-intercept. y = x^2 + x -2      Log On


   

Question 172244This question is from textbook Introductory Algebra
: Graph the quadratic equation. Label the ordered pairs for the vertex and the y-intercept.
y = x^2 + x -2 This question is from textbook Introductory Algebra

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%2B1x%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=%281%29%5E2-4%2A1%2A-2=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%281%29-sqrt%28+9+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B1x%2B-2 can be factored:
1x%5E2%2B1x%2B-2+=+1%28x-1%29%2A%28x--2%29
Again, the answer is: 1, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-2+%29


The lowest point is the vertex.