SOLUTION: 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. Create thr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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. Create thr      Log On


   

Question 51310: 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.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Notice the THREE parts to this solution:
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CASE I:
Discriminant is positive: x%5E2-4+=0
There are TWO real solutions. The implication for the graph of y=x%5E2+-4 is that the graph crosses the x axis at TWO points.
graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2-4%29

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CASE II:
Discriminant is zero: x%5E2-4x%2B4+=0
There is ONLY ONE real solution. The implication for the graph of y=x%5E2+-4x%2B4 is that the graph touches the x axis at only one point, but it does NOT cross the x axis.
graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2-4x%2B4%29

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CASE III:
Discriminant is negative: x%5E2%2B4+=0
There are NO real solutions. The implication for the graph of y=x%5E2+%2B4 is that the graph never touches nor crosses the x axis.
graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%2B4%29

This is a VERY important concept, especially with graphing calculators!! Congratulations on an excellent question!!

R^2 at SCC