SOLUTION: Hello again! I really need help with this problem. Could someone kindly help me? The class is working with Quadratic functions and graphs – I'm supposed to find the vertex and

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hello again! I really need help with this problem. Could someone kindly help me? The class is working with Quadratic functions and graphs – I'm supposed to find the vertex and       Log On


   

Question 18493: Hello again!
I really need help with this problem. Could someone kindly help me?
The class is working with Quadratic functions and graphs – I'm supposed to find the vertex and intercepts , then sketch its graph. l really need help.
y= x^2 -4x -12
This is a head-scratcher for me. Thanks for all of the help. It is appreciated.
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-4x%2B-12+=+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=%28-4%29%5E2-4%2A1%2A-12=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-4%29-sqrt%28+64+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-4x%2B-12 can be factored:
1x%5E2%2B-4x%2B-12+=+1%28x-6%29%2A%28x--2%29
Again, the answer is: 6, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-12+%29

Hope this helps!