SOLUTION: Somebody please help. The graph has to be a real life situation with numbers to make it, I think. I posted the question from my professor, not sure if I completely understand what

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Somebody please help. The graph has to be a real life situation with numbers to make it, I think. I posted the question from my professor, not sure if I completely understand what       Log On


   

Question 36426: Somebody please help. The graph has to be a real life situation with numbers to make it, I think. I posted the question from my professor, not sure if I completely understand what I need. I know I need a graph and some numbers, that's about all I really know. Please help. Any help would be greatly appreciated.using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminate is b2 - 4ac. This discriminate can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. )
• Explain what the value of the discriminate means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminate. Then, graph the corresponding equation.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If discriminant is >0 the quadratic has two Real Number roots.
If discriminant is 0 the quadratic has two equal rational roots.
If discriminant is <0 the quadratic has two imaginary roots.
Example:
y=ax^2+bx+c
If a=1,b=1,c=-2 the quadratic has two real number roots, as follows:
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

Hope this helps.
Cheers,
Stan H.