When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what this value means to the graph of y = ax2 + bx + c.
Please see the attached file for the complete solution.
For ax^2 + bx + c = 0, the value of x is given by:
If discriminant is b^2 - 4ac=0, then x=-b/2a
If discriminant is b^2 - 4ac>0, then (see attached)
If a quadratic equation with real-number coefficients has a negative discriminant, ...
Discriminants are investigated. The solution is detailed and well presented.